The former Nancy and West Brom striker was unsurprisingly replaced by Georgios Samaras just before the hour mark, and although Robson opened the scoring from the spot, United substitute Jon Daly equalised before skipper Darren Dods headed a last-gasp winner.
It was United's first win over Celtic in 10 years and it prevented Tony Mowbray's leapfrogging Rangers at the top of the SPL table.
With two wins in the last 10 games, the spotlight fell again on Mowbray's biggest signing, who has scored only twice in nine appearances, both against St Johnstone at Celtic Park in August.
However Robson, who recently returned from an eight-month groin-injury lay-off, empathised with Fortune.
"It's not easy, Marco is coming back from injury, as am I, and it just doesn't happen like that," the Parkhead midfielder said.
"It's hard and I know how Marco feels because I'm not 100% myself.
"But when you are at a club like Celtic you just have to try and ignore that and make sure you are at your best.
"You need to make sure that you get goals and Marco will keep trying and do a good job for us."
Mowbray again put up a sterling defence of Fortune, who struck five goals in 18 games under the Englishman on loan at West Brom last season.
"Fortune has had 10 weeks out," the Celtic boss said. "If you know anything about football, injuries knock the confidence of footballers and he needs to get himself back up to speed.
"It's going to take time, you can't just do that with just training.
"It's going to take games and that's why he is getting some minutes on the pitch at the moment.
"But I have every confidence in him. Once he is up and running he will be fine."
United manager Craig Levein, again refusing to add to speculation linking him to the vacant Scotland post, was glad to see Daly make such an impact in his first competitive appearance since recovering from a knee injury that had kept him out since April.
The Tannadice boss is hoping his injury list continues to improve.
"We had a lot of people out but the strength in depth of the squad is pleasing," he said.
"Let's hope we don't have any more injuries as we are getting players back.
"We haven't played brilliantly at home this season, our away performances have been better and I felt we owed our supporters something.
"They went away home happy which was really important to me."