James Hayter's fifth goal in as many games looked to have won three points for Rovers but Angel Rangel struck in stoppage time to claim a share of the spoils.
Rodgers said: "The equaliser at the end was a great reward for the players. I was pleased with the battling spirit we showed and it underlined our mental courage and resilience.
"Doncaster are a good side and this is a really difficult place to come and get a result.
"They are normally a team that like to pass and move the ball and often dominate other teams but they had to sit back against us.
"We missed chances early on that might have opened up the game and we just had to keep faith and keep passing the ball. We deserved something from the game and it could be a vital point come the end of the season."
Source: PA
Source: PA