The Serbia international striker twice went down with an ankle injury before he was replaced after 80 minutes by Joe Bryan.
Parker said: "It doesn't look great, at this present moment in time.
"It's too early to say. We'll scan him (on Sunday) and see where we are. He's injured himself pretty badly.
"(If) you lose someone who's scored 18 goals, it's never going to be easy."
Mitrovic's injury was the only low point for Fulham, who had never before won at the KCOM Stadium.
Parker was, though, left grateful to a match-defining contribution from Ivan Cavaleiro, whose flash of magic after 29 minutes settled an otherwise lukewarm encounter.
The Portuguese, who this week signed a permanent four-and-a-half-year contract from Wolves, looked in a fairly innocuous position on the left of Hull's penalty box but Cavaleiro had other ideas and delivered a precise, curling strike with his right foot which ended up in the top right-hand corner.
Parker, whose side consolidated their position in the Sky Bet Championship play-off places, said: "Ivan's a matchwinner. He had one slight opportunity and he showed his brilliance."
He added: "The first half, I thought we played really well. We had a controlled way about us.
"Hull are probably the best counter-attacking side in the division and I thought we did really well to nullify that – even if it meant giving up a bit of possession.
"The second half turned into a typical Championship game – it was not vintage by any stretch of the imagination.
"We realise how tough this division is and at times we've shown how brilliant we can be this season.
"On the flip side, we can be a bit inconsistent but we showed another side to us here.
"We dug in and showed massive character. We've just got to keep picking up points. We ultimately need to worry about ourselves."
Head coach Grant McCann admitted Hull had under-performed.
With influential wingers Jarrod Bowen and Kamil Grosicki ineffective, McCann's men looked short of ideas going forward.
McCann said: "We didn't deserve anything.
"The game was scruffy, with two teams playing nowhere near their best.
"In the first half we were slow in our tempo and build-up play – the second half we were better.
"Both teams would have been quite happy with a draw but them taking the lead probably distracted us a bit.
"A moment of quality has won the game – it's as simple as that."
Hull also have play-off aspirations – they remain three points off the top six – but they have now lost back-to-back league games at home.
McCann said: "Jarrod was quiet, Kamil was quiet.
"The attacking players were a wee bit quiet in the game and Fulham scored a worldie to win the game.
"I don't think there was any rhythm in the game from minute one – it was a bit stop-start. The difference was that tremendous goal from Cavaleiro.
"The frustration is back-to-back defeats at home.
"We need to try and find a bit more consistency at home. What's important for us at home is to score first.
"We'll just keep going. With 19 games left, there's a long way to go. One thing about this group is that we can respond."