Blues were forced into playing for 66 minutes with just ten men after Mehdi Nafti was sent-off for a reckless challenge just 24 minutes into the match at St Andrews.
Blues winner came from Camerone Jerome just a minute into the second half and they were forced to defend doggedly after the goal to keep up their unbeaten league record.
"I'm grateful for the spirit that the players showed but we know we can play better," McLeish said after the 1-0 victory.
"It wasn't pretty but hats off to the 10 men who went out there in the second half, dug deep, rolled their sleeves up and scored a fantastic goal.
"I think Doncaster passed it well and it was difficult for our midfielders to get close to them. But we defended well and had a good, solid back-four display."
The Blues boss also said he had no complaints with the decision to send-ff Nafti: " It was a sending off, no doubt," he said.
"Mehdi has been out for three weeks and he looked a little tired.
"It was a bad challenge."