O'Donnell and his team-mates have been drawn to face Irn-Bru First Division rivals Cowdenbeath in the semi-final of the competition at Central Park on Sunday, October 14.
Jackie McNamara's team have been tipped as favourites to win by bookies after Rangers were knocked out by Queen of the South, who will now go on to play Arbroath.
But the former Celtic kid expects a difficult outing against the club managed by ex-Hearts, Wolves and Scotland midfielder Colin Cameron.
He said: "We haven't played Cowdenbeath yet this season. We play them this Saturday so we will know a bit more about them after that. But I am sure it will be a tough tie.
"It's the only all-First Division semi-final. They deserve to be there every bit as much as us and are at home. I am sure it will not be straightforward, but we are looking forward to it.
"The bookies might have us as favourites – but I'm sure they had Real Madrid as overwhelming favourites to beat Manchester City on Tuesday night and they only just sneaked it. I don't worry about odds too much."
O'Donnell, meanwhile, has stressed that going all the way in the Ramsdens Cup will NOT impact on table-topping Thistle's ambitious bid to win promotion to the SPL.
He said: "The season has gone brilliantly for us so far and we are looking to keep that going. To lose just one game out of nine [away to Hamilton in the League Cup], disappointing though that loss was, has been beyond our expectations.
"It is just down to hard work. That, and the fact the gaffer has brought in players who have improved the squad. We were decent last season and perhaps under-achieved. Hopefully we can stay up there and challenge for the cups and the league."
THE ex-Parkhead youth star added: "You hear people in England talking about how they could do without the extra games when the cups are being played. I don't understand that. The fans at Thistle deserve a run in the cup – they haven't been to a final in some time.
"They got knocked out of the semi-finals of the Ramsdens Cup a couple of years ago. Hopefully we can win our next game against Cowdenbeath and get to the final. Who knows?
"If we were to get to the final and then win it, it would give us a great boost if we were still challenging. Winning is always a boost, whether it is in a league game or in a cup final.
"The cup final is near the end of the season and perhaps winning it would be enough to get us over the finishing line if we are still challenging for the First Division title.
"We are just taking it one game at a time just now and our immediate goal is to beat Cowdenbeath this weekend and keep our good run in the league going.
"But getting to the final of the Ramsdens Cup and winning it is a definite goal for us all this season. It would be great to give the fans something to really shout about."