The Rossies face an All-Ireland qualifier against either Armagh or Tyrone after they failed to retain their crown in Dr Hyde Park yesterday.
And O’Donnell said in the aftermath that his side will be rank outsiders against either Ulster representative.
He said: “It will be very difficult for us. I always said our best chance was to go the front route.
“Facing Armagh or Tyrone, there’s probably only one conclusion. Let’s be realistic,” he added.
O’Donnell felt his side needed to score more in the opening half when they had the wind and rain at their backs but, ultimately, the fact they managed only two points after the restart put paid to their hopes of retaining their title.
O’Donnell said he set a target of four points in the second-half against the wind but they only managed half that as their quest for a first win in a decade over either Mayo or Galway goes on.
Donie Shine fought a lone battle up front in the second-half but the Mayo defence managed to contain him after Shine caused huge trouble in the opening half.
O’Donnell lamented their failure to pick off more scores in the opening half when they had Mayo on the ropes.
“I didn’t think it was enough [they led 0-9 to 0-5]. The breeze was very strong and I didn’t think we played well enough in the first-half. I thought we needed to get four in the second-half and we didn’t, we got two in the second-half. I said we’d have to reach a new level and we didn’t. We played poorly.
“But it was a game that was there for the taking – we definitely could have snatched the draw, We turned over the ball too many times. We’re very disappointed with our performance.”
The former midfielder said that while he felt his side could have produced more, he had no qualms about the merit of Mayo’s win.
“The best team won. We just weren’t hungry enough, and we’re very disappointed with our display.”
O’Donnell said he didn’t blame Donie Shine for not finding the net after 50 minutes with one of the few goalscoring chances in the game. “The chance came from a lucky break, it came out of the blue. Mayo had a chance the other side so these things balance.
“We turned over the ball up the middle too often, we had every opportunity to maybe create a score near the end but turned the ball over.
“Silly stuff like that [cost us]. Again, Mayo were probably a little bit stronger and we just weren’t strong enough to break the challenge at times.
His side will have an extra week to prepare following the draw between Armagh and Wicklow last week, but that was of little consolation to the Roscommon manager.
“When you lose, you lose. This was a game we wanted to win and unfortunately we didn’t deliver,” he said.
O’Donnell said that while the incessant wind and rain made it difficult to play football, he wasn’t using them as an excuse to relinquishing their crown.
“Conditions were very bad. They probably weren’t as bad in the last 10 minutes, but when we started the game they were horrific. It was unfortunate really, but they were the same for both teams and Mayo adapted the better, fair play to them.”