Morton stunned the Scottish champions with a 1-0 third-round victory at Celtic Park courtesy of Dougie Imrie's extra-time penalty.
And Fitzpatrick believes the famous win owed much to their team spirit and work ethic.
"It was just one of those nights," said Fitzpatrick.
"Celtic never really performed. We sat in and rode our luck a wee bit towards the end, but it was one of those nights where I think we could have played for ages and never conceded."
Morton's performance on Tuesday night was in stark contrast to their Championship form so far this season, which sees them second bottom of the table.
"I hope this is a platform to kick on," Fitzpatrick said. "The manager said to us after the game that if we dig in like that in every game we play then we'll win more than we lose.
"Sometimes obviously the mentality's different when you go to Celtic Park rather than a normal league game, but we need to try and use the team spirit we had last night to help us climb away from the bottom of the table.
"Everybody knows you're going to be under pressure and have to work hard and defend for the majority of the game when you go to Celtic Park, so that mentality is instilled before a ball is kicked.
"In league games you're maybe expected to go out and attack a bit more and maybe players don't concentrate just as much defensively.
"But that's something we'll have to work on in the league, and I hope we can take the performance from last night into our league games coming up."
With Celtic manager Neil Lennon fielding a strong side for the tie, former Motherwell and Ross County man Fitzpatrick felt the effort levels of Alan Moore's side had more to do with the result than Celtic's approach.
"They possibly took us a bit lightly, I don't know," he said. "With all the big games they have, I don't know what their mentality would have been for Morton.
"But I think we did really well just to dig in. We fought for each other and we restricted them from creating a lot which maybe frustrated them. Later on when they started just throwing high balls into the box they got a couple of openings, but I don't think apart from that they had too many chances.
"I would have thought that possibly some of the guys who hadn't been playing for Celtic would have come in and performed better than the ones that are guaranteed to play every week as they would be more determined to perform well in front of the manager.
"But considering it was only really (Fraser) Forster, (Anthony) Stokes and (Kris) Commons that were out from their first team, they put out a strong team which showed us a bit of respect and we did well to stand up to them."