After suffering their heaviest home defeat of the campaign on Sunday as Motherwell eased to a 5-1 Firhill win, Alan Archibald's side kick off 2014 against the champions seeking a much-needed three points to ease the pressure in the SPFL Premiership.
A recent winless run has seen them fall to 10th in the table and O'Donnell knows they must pick themselves up quickly if they are to stop the rot on derby day.
He said: "The Motherwell game was very disappointing, but we have to lift ourselves, we have got a huge game that we have to turn up for.
"We were the better team for the first 20 minutes against Motherwell, but when they scored we capitulated.
"It is the first time this season we have looked that poor. We need to have a hard look at ourselves.
"One game like that in six months is not the worst, but it is still not good enough and we have to make up for it quickly.
"If we react well, we can go and challenge Celtic and give them a hard game.
"But if we turn up like we did against Motherwell it could be bad. We have to work on it and get it out our system.
"Hopefully we'll be far better. We have to give a much better account of ourselves."
After making an impressive start to life back in the top flight, Thistle have found recent weeks hard going as they have struggled to pick up points and suffered a series of morale-damaging defeats.
A trip to Parkhead is far from the ideal pick-me-up, but former Hoops youngster O'Donnell is determined to see a quickfire improvement.
He said: "I am hoping that tomorrow takes care of itself but you never know what can happen. I wasn't expecting Sunday to go like it did.
"We have given a good account of ourselves in the Premiership so far so hopefully we can put it down as one bad game and kick on in the new year and start winning again."
He went on: "I have played at Celtic Park in a couple of youth games, but it will be different this time
"Hopefully there will be a good atmosphere there and a good crowd.
"We owe the Thistle fans a performance after Sunday."
Just hours after their Firhill thrashing, boss Archibald moved to bolster his squad for the second half of the season with the capture of former Falkirk star Lyle Taylor.
A lack of firepower has cost the Jags dear in recent weeks as they have relied heavily on Kris Doolan for goals.
Archibald is eager to see more new faces arrive at the club during the January transfer window as he contends with injuries to Isaac Osbourne and Sean Welsh and the Thistle gaffer is pleased with his first addition.
"Hopefully he (Taylor) will bring goals. He was successful in his spell at Falkirk," he said.
"His attributes are his predatory instinct to go and score goals and he knows where to be at the right times. He did that at Falkirk.
"He's also got a good touch and he can give us something different to what we've got here.
"It gives us a bit of competition and hopefully it gives the rest of the group confidence that we are signing good players and it can push us on."