"It always is (dramatic) with United," Ole told MUTV. "That's part of being a United player. You need talent and skill and all that, but character and attitude are things the manager is always looking for in players.
"They bounced back every single time, they never gave up. That's the history of United and I think today they've shown they can be a part of it."
Solskjaer was quick to pay tribute to Villa's sterling efforts in an epic encounter, but felt the victory was fitting reward for his side's season-long efforts.
"I thought it was a great game," he said. "In the first half they were the better team for long spells. Luckily we got a goal before half time so the boys came in believing they could do it and they came back twice more.
"I thought their attitude was brilliant, so they deserve it. The season has been a long one, but they've done fantastically well."