The result at Loftus Road was the Welsh side's fourth consecutive defeat.
Despite sitting 10 points above the relegation zone, Rodgers wants his team to secure their Premier League safety sooner rather than later.
"I can only apologise to our supporters," the Irishman told BBC Sport. "I have never had to do that before but we were poor. We beat ourselves.
"It's been a terrific season but we need to get over the finishing line.
"What I have said to the players is that we're not mathematically safe. We need to re-group and if we can do that then it will have been an iconic season for us."
The Swans host struggling Blackburn Rovers in the league on Saturday.