Brazil forward Pato, the club's record signing when he joined from AC Milan in January, had to score on Wednesday to keep Corinthians in the Cup after the quarter-final ended 0-0.
But his clipped spot kick was easily saved by his former Milan team mate Dida and Gremio qualified for a last four clash with Atletico Paranaense with a 3-2 shootout victory.
Goias play Flamengo in the other semi-final.
"I accept the criticism over my mistake," the 24-year-old Pato said in a statement.
"But I want to make it clear that I wasn't negligent or remiss. I made a mistake but I didn't try to dink it, or try to be fancy.
"I am a man, I take responsibility and I will continue to be here for Corinthians as we try to finish the year in a better position."
The Lance newspaper reported that Corinthians would listen to offers for the striker, who has been unable to secure a regular place in the side, in the next transfer window.
Corinthians, last year's Copa Libertadores and Club World Cup champions, are 12th in the Brazilian league, only seven points above the relegation zone with eight games to play.