Striker Paul Heffernan put Rovers ahead at the break with defender Jonathon Grounds levelling the score in the second half.
Said Rovers' boss Sean O'Driscoll: "We got better and better as the game went on and could have won it in the end.
"I think Neil (Sullivan) made one save at the start of the second half. But credit to them they are rejuvenated side and it was maybe the wrong time to play them.
"But I thought we handled it well without hitting the heights of previous games.
"We are eight unbeaten now which is good and we just want to keep it going.
"We have always been a passing side but we have improved on all the things that the good sides do when they are not playing really well."
"It was unfortunate that we didn't hang on for the three points, but, like I said, we need to give Norwich some credit and I think a draw was a fair result.
"They played with ten men behind the ball and we were trying to pass the ball on a difficult pitch through the majority of their team.
"We are not a team who goes route one so it was difficult."
Said Norwich boss Bryan Gunn: "I thought that we might go on and win it after we'd equalised but Doncaster are a good footballing side and they continued to play and create chances.
"But some resolute defending and some great goalkeeping saw us hang on for a point."
n Rovers are set to complete the signing of Hibs forward Dean Shiels, subject to a successful medical.
"He is a good age and we feel that we can afford the money that we've paid for him," said O'Driscoll.
"Hibernian were going to lose him on a Bosman - we lost Paul Green on a Bosman and it is not a nice feeling.
"They aren't playing him at the minute because he won't sign a contract.
"He's an international player (Northern Ireland) who can play in several positions and he's technically very good and he wants to play in the Championship. Since we made contact he's done his homework on Doncaster. He's a bright boy and desperate to come and play."