The defeat was Atlanta's third in a row and fourth overall in an NFL campaign that began with hopes of a Super Bowl appearance.
Their 1-4 start has made a playoff berth seem unlikely, but Gonzalez is refusing to give up on the possibility of leading his side into the post-season.
"What are we going to do, sit here and feel sorry for ourselves? I'm not going to put my hands up and say the season is over," Gonzalez told The AP.
The Falcons have a bye this week and will return to action against the Tampa Bay Buccaneers on October 20.