Raheem Sterling's first-half goal was enough to earn a 1-0 home win.
"It's brilliant for the players. They thoroughly deserved it," said Rodgers after the game. "You come off the back of an international week. It's never easy with the players all being away, but I thought the first half we were excellent.
"Our control and domination of the game was very good. The second half we started well and then on towards the last 20 minutes we needed to manage the game a wee bit better and manage the ball better.
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