Bamford, a 70th-minute replacement for Junior Firpo, marked his return after being ruled out since mid-September with an ankle injury by snatching Leeds a point in the fifth minute of added time.
Brentford pair Shandon Baptiste and Sergi Canos had turned the game on its head with goals early in the second half after Tyler Roberts’ first Premier League goal at Elland Road had given Leeds an interval lead.
Bielsa was clearly grateful for Bamford’s second goal of the season, which lifted his side up to 14th place in the table, six points clear of the relegation zone.
“The players that are used to scoring normally, they are in the right place at the right moment,” Bielsa said. “What you value about this goal is the opportunism of it.
“Patrick scored a goalscorer’s goal. The time on the pitch he came on made it difficult to find the ball, but finally he gave us the equaliser, that is very valuable for our expectations, given how we got it.
“Before the game, it wasn’t a good result, after the first half it wasn’t as well, but when the game finished we need to value what we got.”
Leeds had been in control at the start of the second half and Brentford goalkeeper Alvaro Fernandez’s one-handed save prevented Luke Ayling’s header from extending their lead.
But the visitors stunned Leeds with two goals in seven minutes through Baptiste and then Canos and appeared to be heading for a fifth league win of the season.
Bielsa added: “Drawing the game the way we did changes the flavour, but if you look at the game in its general context, we should have won it.
The Leeds manager said he was waiting to learn the full extent of the injuries sustained by skipper Liam Cooper, forced off in the 15th minute, and Kalvin Phillips, who was withdrawn in the 55th minute.
Brentford boss Thomas Frank could not hide his disappointment, but was full of praise for his side, who were without Ivan Toney after the five-goal striker tested positive for coronavirus.
Frank said: “At this moment I’m not celebrating. What I will celebrate is the performance.
“A top performance. First half, really good start, first 10, 15 minutes then Leeds were on top and we defended very, very well.
“We gave nothing away except for the goal. Besides that, nothing. Second half, we stepped up, pressed a bit higher and scored two very good goals.
“We were in complete control. I would say they didn’t create anything and last-minute a second set-piece goal. That’s a tough one.”
Bees forward Canos fell to the ground after appearing to be hit by something thrown from the Leeds end while celebrating his goal.
Frank added: “I haven’t spoken to him and I don’t know what happened.”