Donegal manager Rory Gallagher said his side had "dug themselves out a difficult position" against Fermanagh after playing the entire second half with 14 men.
Full-back Neil McGee was sent to the line just before half-time when he led with his arm into Ruairi Corrigan's face after securing possession.
Referee Maurice Deegan also awarded a penalty but Sean Quigley missed the kick and Donegal ran riot after the break to win 2-12 to 0-11 despite being a man down.
"I'm pleased to win," Gallagher told RTÉ Sport. "I thought we dug ourselves out of a difficult position, being a man down in the second half.
"Overall, I thought we were much the better team, barring a 10 or 12-minute period coming up to half-time.
"You expect that. Fermanagh are a quality team.
"We're pleased with how we played overall. Disappointed to lose a man and to get a couple of yellow cards early on but we have to work on that."
"The first 18 minutes of the game we played really well and had 1-5 on the board but we probably got a bit casual and complacent.
"The second half was very controlled. We got ourselves into a great position, went 2-10 to 0-08 up and after that it was just a matter of seeing the game out.
"We're pleased to be through but I wouldn't like to play with 14 too often."
Gallagher said McGee felt he had just "shrugged off" Ruairi Corrigan in the incident that led to the Donegal man's dismissal.
Due to a retrospective ban sustained following the League game against Kerry, McGee is now facing a two-match suspension that would rule him out of the Ulster semi-final against Monaghan and the final, should Donegal get there.
"Niall feels that the referee had blown a free out and then he tried to shrug yer man off," said Gallagher, though he admitted: "It wasn't easy to see from where I am."
"If he's going to be out, it's very disappointing. He's a huge player for us.
"I didn't realise it was possibly two games but we'll have to deal with the game in 13 days' time first."
The Sunday Game panel of Ciaran Whelan, Pat Spillane and Joe Brolly strongly disagreed, arguing that McGee's red was well-deserved.
Fermanagh boss Pete McGrath thought that Odhran MacNiallais' second goal of the day, to send Donegal five clear in the 44th minute, was pivotal.
"It infused them with energy and confidence," he said. "They're an experienced team, so when they saw that bit of daylight, they knew how to manage the game.
"I thought we stood off Donegal far too much in the first 15 minutes. We let them get a major foothold and they were dictating things.
"The last 20 minutes of the first half, we took the game to them, got to within two points and could have gone in a point ahead. But penalties are scored and penalties are missed and that's the way it is.
"We got the first score in the second half and were going toe-to-toe but Donegal's second goal was critical and punched a bit of the confidence out of us."We had a lot of possession but we were running into trouble or shots were dropping short and the conviction seeped out of us."
Despite the defeat, the Down native is confident that Fermanagh can repeat their exploits of last season, when they progressed through the qualifiers to an All-Ireland quarter-final against eventual champions Dublin.
"We certainly can do it again," said McGrath. "I said after we were beaten last year that we'd be playing football in August and I'm saying that again.
"I think we're a better team now than we were last year.
"We're bitterly disappointed at losing but we'll take a lot of positives out of the performance."
"On any team's journey you're going to get days like this. This is still a young team, a relatively inexperienced team.
"We'll regroup and look positively to a qualifier in 13 days' time. It's essential for this group that we make the summer as long as we possibly can."
