Rodgers said, "It's been too long [since they last won] but I thought we were excellent tonight, with our intensity and pressing in the game.
"It was a great night for the players and brilliant for the fans. I said if we could get a result tonight then we could push on.
"We've got a lot of technically gifted players but you can't win football matches without the desire to win the game
"In key moments in other games we haven't defended well but we have tonight and we've kept a clean sheet, which is also very important."
He added: "When you don't win games it comes on to you. We had a horrendous summer, that's the reality of it and that continued into the start of the season.
"I just had to remind the players of their ability and continue to support them. They have bags of resilience. We just needed to turn that corner tonight and we did that. We have to back it up against Bournemouth now."