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The captain scored twice in his first game since announcing he would move to Major League Soccer in the summer.
If Liverpool reach the final, which is on Gerrard's 35th birthday on 30 May, it would be his last game in England.
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"There would be no better way for it to end," Rodgers said.
"Steven was outstanding. He gave a brilliant individual performance. He scored two and if he was a more selfish player he might have had a hat-trick."
Midfielder Gerrard, who was expected to be on the bench, started the game and took his tally to 182 goals in 696 appearances for Liverpool, the only club he has played for.
"He's a world-class player who might be getting older, and at times the legs fatigue a bit, but he's absolute top drawer, a top-class player," Rodgers told BBC Sport.
"He has that real sprinkling of quality that this team needs. His two goals tonight were fantastic."
Gerrard said of ending his Liverpool career at Wembley: "Hopefully that will be the case. It's what dreams are made of.
"I grew up loving the FA Cup and this is my last time, so I want to make the most of it and go all the way."
Adebayo Akinfenwa equalised Gerrard's headed opener, but the former England captain curled home a superb free-kick in the 62nd minute to secure a fourth-round tie at home to Bolton.
AFC Wimbledon boss Neal Ardley said: "With a bit more nous, we could have got at least a draw, but we got done by a world-class player."
Liverpool boss Brendan Rodgers said the FA Cup final would be a "wonderful send-off" for Steven Gerrard after his side beat AFC Wimbledon 2-1 to reach the fourth round.