The Reds extended their unbeaten streak to a seventh match in some style at Craven Cottage, twice coming from behind before eking out a 3-2 victory courtesy of Steven Gerrard's stoppage-time penalty.
"It was a very important win for us tonight," Rodgers said. "Obviously after the game at the weekend when we were outstanding [beating Arsenal 5-1], we had to show some different qualities tonight.
"One of them was character and this was a wonderful demonstration of the wonderful togetherness of the group.
"You're always pushing and you're always looking to get something. For me, it's never over until the whistle goes.
"Yes, they were disappointing goals. We've defended poorly at times this season, it has not been structurally but mistakes and individual errors.
"But thankfully we're a very aggressive and offensive team going forward, so we have goals in the team.
"That's something I've been trying to build since I've been here. When I arrived into the club, the complaint about the team was that they didn't score enough.
"Now we know we can go to any ground, or at home, and get goals. Obviously tonight the goals got us the three points rather than our defending."