Two own goals from Guy Demel and Joey O'Brien were added to by strikes from Mamadou Sakho and Luis Suarez as the Reds moved to second in the Premier League table with a performance that pleased Rodgers.
"I thought my team were excellent today," he told BBC Radio 5 Live.
"We scored four goals, and maybe could have had another four. We were relentless in our attack.
"What really pleased me was our response when it went to 2-1 through an own goal. We responded well, controlled the game and made the chances which swung the game back in our favour."
Liverpool's next fixture sees them travel to London to take on Tottenham Hotspur at White Hart Lane next Sunday.