Ben Whiteman’s late penalty secured victory after Peter Clarke had cancelled out the midfielder’s deflected opener at the Keepmoat Stadium.
The result was harsh on Sky Bet League Two club Oldham, who gave as good as they got against a side from the division above them.
“It’s a credit to the boys,” McCann said. “It’s nice to be on the end of a late goal to win the game instead of a late goal costing us the game and I thought we showed tremendous character to do that.
“It means everything: for the football club, financially, it changes our lives a little bit.
“If we can be the lowest league team left in the tournament there’s an extra incentive.
“The boys have delivered, they were outstanding - I thought we controlled the game for large parts but in an FA Cup tie you’re always suspect to a side coming strong for 10-15 minutes which Oldham did but the reaction from us was fantastic.”
Referee Peter Bankes awarded the decisive penalty after a lengthy consultation with his assistant, before concluding that Clarke had handled the ball during a goalmouth scramble.
“The fourth official and the linesman were adamant it was a penalty,” McCann added.
“All of my staff and players were adamant it was a penalty. I need to see it back again.”
Rovers had the better chances in a drab first half, with James Coppinger’s volley producing a fine save from Dan Iversen and Clarke producing a dramatic goal-line clearance after John Marquis had rounded the Oldham goalkeeper.
The home side took the lead after 68 minutes when Herbie Kane laid the ball off for Whiteman and his 20-yard effort deflected off Clarke to deceive Iversen.
Chris Missilou struck the frame of the goal for the visitors before Gevaro Nepomuceno’s 20-yard free-kick after 84 minutes caused chaos in the Doncaster box and Clarke pounced in front of a delighted away end containing 3,800 Latics fans.
But moments later the contest was turned on its head again as Bankes pointed to the spot after consulting with his linesman, with Clarke deemed to be the guilty party. Whiteman calmly converted the subsequent spot-kick.
The 37-year-old Clarke’s eventful afternoon was still not done as he was sent off in stoppage time after a coming-together with Marosi.
Oldham interim boss Pete Wild, who insisted post-match that he knew nothing about speculation linking former Manchester United midfielder Paul Scholes with the position, felt his side had been unlucky.
“Clear as day - that’s never a penalty in a million years,” Wild said after being shown a replay of the incident.
“They’ve had a lot of chances in the game - they’re always going to score one of them and they did.
“We stayed resilient, got a goal of our own and then it could go either way, and it’s disappointing that a controversial decision has won the game.
“We’ve enjoyed this competition and had some good days out but I’m sure we all want some good days out in the league now.”
On Clarke’s sending off, Wild added: “I think their keeper has got him sent off by rolling around and with his antics, which at this level is poor.”