Steven Gerrard's second-half strike looked to have secured all three points for the Reds, but Phil Jagielka fired a volley into the top corner in stoppage time to earn the Toffees a share of the spoils.
Rodgers told BT Sport: "The players were brilliant. We were clearly the dominant side in the game, but sometimes you don't get what you deserve in football.
"But for a wonder strike at the end of the game we would have got the three points. But they get their point and we are happy with the performance, if not the result."
Liverpool are currently 12th in the Premier League after their draw today.