Jefferson Lerma scored the winner as 10-man Colombia claimed a 1-0 win over Uruguay at the Bank of America Stadium in Charlotte, North Carolina to progress to Sunday's final.
Uruguay, 15-time champions, had been one of the pre-tournament favourites and beat hosts United States and five-time World Cup champions Brazil en route to the last four.
"Uruguay was in a clear condition to win this match if you assess the individual talent in each squad," Bielsa told reporters.
"I manage the team that, in my opinion, had the stronger individual talent vis-à-vis the opponent, and we weren't able to make the difference that I thought we were going to make if you compared both formations.
"I am personally liable for not achieving the result, despite having these players that were capable of being superior than the opponent.
"We were not able to seize our extra man advantage, and when a team wins with less individual talent, logically, the manager that is coaching the weaker team shows that he is superior than the coach that had the best players."
Uruguay had a number of chances to score in the first half but struggled to create opportunities after Colombia's Daniel Munoz was sent off just before half-time.
"The first half, even if we didn't dominate possession, it was very even, and we should have made the difference. With one man down in the second half for Colombia, the match was completely interrupted," Bielsa said.
"It was constantly start and stop. We should have created more chances and caused damage to the opponent. In the last minutes, they could have scored because they had clear chances.
"But we tried every possible way, every possible path."
After the match, Uruguay players clashed with Colombia fans in the stands, and governing body CONMEBOL has opened an investigation into the incident.
Uruguay next face Canada in the third-place playoff match on Saturday.
