The Whites looked comfortable as they led 1-0 at half-time, but a mad 15 minutes saw them suddenly trailing 2-1 and looking all over the place before they pulled their game back together and took a point thanks to the dramatic Bamford goal after Raphinha's corner had been flicked on by another player making a successful return from injury, Luke Ayling.
The point could have come at a cost as just when Leeds welcomed two of their key players they lost two more with Scotland international Liam Cooper and England's Kalvin Phillips both limping off during the game.
But the value of the draw was accepted by Bielsa as his team have edged up the Premier League table again to be 14th and he reckoned United dominated much of the contest.
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He said: “Before the game it wasn’t a good result. After the first half it wasn’t as well, but when the game is finished we value what we earned.
"To have drawn the game the way we did, it changes the flavour, but, if you look at the game in its general context, we should have won it.
"We conceded the first part of the game, but without receiving any goals. From the initial 15 minutes onwards, we had a good half an hour.
“In the second half, we started it well and we had incomings and outgoings of Luke Ayling and Kalvin Phillips, where we were a few moments without them.
"After Kalvin went back on and came back off, that made us lose organisation. But, it shouldn’t have been this way.
“In those 15 minutes in the second half we did receive the goals, but the final 30 minutes there were a lot more difficulties, but with a lot of perseverance to attack.
“I think we ended up getting a result that was fair on one side and insufficient if you look at the whole game.
“We dominated two thirds of the game and we duplicated the amount of dangerous situations that we had, compared to the opponent.”
Bielsa was pleased with the return of Ayling and Bamford.
He added: "Ayling had a satisfactory game and Patrick scored a goalscorer's goal.
“In the centre of the pitch where he (Bamford) came on, it was difficult to find the ball. But finally, he gave us the equaliser, which for our expectations is very valuable given how we got it.
“The players that are used to scoring are usually in the right place at the right moment. What we value about this goal is the opportunism of it."
Off the back of their late earned win in midweek Leeds set off quickly and were inside the opposition box in the first 30 seconds only for the opportunity to be squandered when Junior Firpo's pass was intercepted as he had opted to move the ball on instead of shoot.
But it was 27 minutes before they managed their first shot as several further promising attacks were ended by crosses that were dealt with by a Brentford back line marshalled by former Leeds favourite Pontus Jansson.
Jansson headed out Raphinha's initial cross in the 27th minute, but a follow-up effort was superb and was met by Tyler Roberts, who slid in for his first goal of the season.
Brentford were hard done to at this stage to be behind, but did not create much themselves in the opening half, aside from a Sergi Canos deflected shot that was comfortably saved by Illan Meslier and a Bryan Mbeumo shot that went well wide.
By this stage Leeds had already been forced into making their first substitution with skipper Liam Cooper forced off with what looked like a hamstring injury. Jack Harrison came on for him and a couple of reshuffles followed with Phillips initially moving into the defence before resuming midfield duties, particularly keeping an eye on Bees playmaker Shandon Baptiste.
Buoyed by their goal, United enjoyed their best spell of the game as Roberts came close to a second goal with a well struck shot that was equally impressively saved by keeper Alvaro Fernandez.
It was Roberts again in the thick of the action as he sent a cross-shot wide while Phillips was also off target with a strike from distance.
With a better final ball the Whites could have been further ahead, but they were cheered off with their strong-looking one-goal lead at the break.
The second half initially started where the first had left off as Ayling came close to a goal on his return to first team action with a near post header from a Raphinha free-kick that was acrobatically saved by Fernandez. Ayling then looked to follow-up only for his second header to be blocked.
But out of the blue Brentford equalised when Rico Henry wriggled away from Stuart Dallas on the flank and found Canos in the box. His effort was blocked, but the ball fell perfectly for the unmarked Baptiste, who beat Meslier with a scuffed shot from the edge of the box.
He had been in the clear with his marker, Phillips, unable to close him down as he had picked up an injury and needed to come off.
The reaction to the goal and losing Phillips was not good from United as from a position of strength the game could have been taken completely away from them in the next 10 minutes.
It was all about striker Canos as he had a goalbound shot well blocked by Ayling, then headed wide when free at the far post and finally scored just after the hour mark, with a fine finish after getting in behind Diego Llorente.
From this position, the game changed again, however, as once they were in front Brentford appeared to concentrate more on time wasting tactics than trying to add to their lead and they did not muster another single meaningful effort on goal.
Their defending was solid, though, even with Leeds now having Bamford on from the bench for his much anticipated return to first team action after his spell on the sidelines.
Dallas had a shot saved as he burst forward from the left-back position he had switched to while Roberts' shot from 20 yards out was comfortably caught by Fernandez. But although they now had almost all of the ball the Whites struggled to create clear chances.
That was until with the game deep into added time they won a corner and with keeper Meslier up in the box to create a distraction Ayling's perfect flick on was met by Bamford's instinctive close range finish to end the game all square.
It was the third time this season Leeds have scored vital injury-time goals at Elland Road and once again it was met by jubilation from another big crowd.
Leeds United 2 (Roberts 27, Bamford 90+5)
Brentford 2 (Baptiste 54, Canos 61)
Sunday, December 5, 2021
Leeds: Meslier; Ayling, Llorente, Cooper (Harrison 15); Dallas, Forshaw, Firpo (Bamford 68); Raphinha, Phillips (Klich 55), James; Roberts.
Brentford: Fernandez; Goode, Jansson, Pinnock; Roerslev, Norgaard, Janelt (Jensen 90), Baptiste (Onyeka 69), Henry; Canos (Wissa 72), Mbeumo.
Referee: David Coote