The Reds trailed when Christian Benteke fired home in the 31st minute but Jordan Henderson equalised in the 47th when he got on the end of a brilliant Philippe Coutinho through-ball before Steven Gerrard converted from the penalty spot after Luis Suarez had been brought down by Nathan Baker on the hour-mark.
Rodgers was extremely positive after the match and full of praise for how his Liverpool side went about things to remain seventh on the table.
"I thought the players were brilliant today. In the first half, we played reasonably well, but got punished with a long ball and it ended up a good finish from Benteke," said Rodgers.
"But second half I thought the players were outstanding with the mentality and the quality in their game.
"We had a lot of shots and were very good offensively. Once it got to 2-1 I thought we could control things. The players were magnificent and it was a great win for us."