Canada made several changes to their lineup for the match and looked the fresher side as they caused Uruguay a number of problems.
Uruguay, ranked 14th in the world, were on the verge of a shock defeat to the 48th-ranked Copa América debutants before Luis Suarez scored a stoppage-time goal to force a penalty shootout, which Bielsa's side won 4-3.
"It wasn't a great performance. The draw, at best, was barely deserved. I think that the opponent head coach's decision to prioritize physical aptitude instead of usual starters was more successful," Bielsa told reporters.
"I went with the usual starters in spite of them being weary. There were ups and downs. The chances created by both teams were even, but in all truth, we didn't play well.
"Regarding this third place, I do think Uruguay is one of the three best teams of this tournament. Even if this tournament came after long seasons and the tiredness affects players, I thought that given our roster, we could have played a bit better than what we showed."
Bielsa's counterpart Jesse Marsch, who took charge of Canada in May, said he was proud of the progress the team had made in a short period, adding: "The players are disappointed in the way that we gave the match away.
"But I was very positive with them. We've been together for a little over six weeks. We came into this match, put some new players on the pitch, played for me against one of the best teams in the world, and dominated the match.
"We're still a young team. If you look at their team, they have experienced players across the board, players playing at big clubs, a lot of experience in understanding how to handle moments. And we're still developing that."
The American also hailed Canada's fringe players for quickly adapting to his style of play despite coming into the match with little game time.
"The beauty was the clarity with which the way that we're playing was executed by the new players that came in," Marsch said.
"It's not so easy to build a tactical model with such short time and under such big stresses against such good opponents and then see them respond and perform and execute at such a high level. So, again, what a positive sign.
"What a great group of guys. What incredible potential we have with this team."
