Rovers started slowly but grew into the game and had more attempts on goal than the Brewers but Liam Boyce scored the only goal in the 47th minute.
“We’re disappointed,” said McCann. “When we play well, I’ll tell you. Today, I thought we were disappointing. But on the whole it’s been a decent start, with three wins from four games.
“It’ll be a good test of character now for the next three games. We’ve got three home games coming up, two in the league and one in the cup, and we want to respond in the right fashion.
“I’ve got no complaints with the result, I thought Burton deserved to win the game. We weren’t good enough. We looked very lethargic and low on energy. We didn’t move the ball as quick as we can. We need to respond very quickly.”
Boyce struck by firing in off the post after super work in midfield from Scott Fraser, who unselfishly played him in.
In an evenly-matched first half, Joe Sbarra and Marvin Sordell went close for the Brewers but it was Rovers striker John Marquis who wastedthe best chance from eight yards.
Rovers threatened an equaliser with Joe Wright thumping a header wide and Mallik Wilks showing pace and trickery down the right to send an angled effort inches wide.
Substitute Paul Taylor almost rescued a point with a free-kick that was saved by Stephen Bywater.
Burton Albion: Bywater, Brayford, Buxton, McFadzean, Turner, Fraser, Sbarra (Templeton 41), Fox, Akins, Sordell, Boyce (Harness 90). Unused substitutes: Hutchinson, Campbell, Hodge.
Doncaster Rovers: Marosi, Mason, Wright, Butler, Andrew, Kane (Blair 59), Whiteman, Rowe, Coppinger (Taylor 59), Marquis, Wilks (May 81). Unused substitutes: Lawlor, McCullough, Anderson, Beestin.
Referee: P Bankes (Merseyside).