However, the Northern Irishman did concede that Liverpool did have some luck when Udinese skipper Antonio di Natale blasted wide of the mark in the dying seconds with a goal ending their run in the competition.
"It is that moment when there is literally 20 seconds left and we've given away the ball. It was very close," admitted Rodgers.
"Hopefully it is a sign we have a little bit of luck going our way because maybe a couple of months back that would have gone in and we would be out of the competition.
"There was no margin for error tonight, I felt we had to win the game because we were in a difficult group against good teams.
"Over the course of all the games, how we have played and progressed through the tournament I think we are deserved winners of the group.
"We can rest well, focus on the league and look forward to next February."