Skipper Josh Simpson put Town ahead with a fine drive but a 43rd-minute header by James Husband gave the visitors a point.
Barker, whose side are now winless in their last four matches, said: "We deserved to win the game to be honest. The players were absolutely fantastic and their energy levels were excellent.
"We felt we could move the ball quicker, with more pace, and that proved right."
Barker was disappointed with the manner his side conceded, as well as losing Simpson to an ankle injury.
He added: "I'm delighted with the way the players put their bodies on the line. But we defended far too deep when Doncaster got their goal. But they got a little bit frustrated at the way we moved the ball around."