The stunning goals of Jordan Henderson and Philippe Coutinho grabbed most of the headlines in the aftermath of a pulsating game at Anfield, but Rodgers was quick to hail their midfield colleague.
Allen, whom Rodgers brought with him to Anfield from Swansea City in 2012, has struggled to hold down a regular first-team place, but a recent injury to Steven Gerrard has seen him afforded an extended run in the side.
"Joe Allen is a very underrated player," Rodgers said in a press conference on Monday.
"He was one of the first players I wanted to bring to Liverpool.
"Joe was incredible versus City. He had so much courage to get on the ball.
"He allows other players to receive the ball. £15 million for Joe Allen was great value for us."
Sunday's victory saw Liverpool move up to fifth in the Premier League table, just two points behind fourth-place Manchester United and three adrift of Arsenal in third.
"It's tight [in the race for fop four]," Rodgers added. "Arriving in there has always been our objective. We want to keep chasing right to the end.
"We had to stay strong during a tough moment. We've found the solutions and we're playing at a high level.
"The mental and physical energy we put into the [City] game after such a long trip [to Besiktas] was unbelievable. Now we're focused on the next game."
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