Whether that will be the case remains to be seen after a chorus of boos greeted Simon Murray's 89th minute strike at East End Park which clinched the aggregate win for the Spiders following the goalless first leg at Firhill in midweek.
While Queen's progress to the final, where they will meet Airdrie for the chance to be promoted to the second tier, the Pars drop into League One, where they will join already relegated Queen of the South next season.
The match summed up a disastrous campaign for Dunfermline, who had defender Efe Ambrose sent off early in the second half and who lacked a cutting edge in attack as they failed to secure their safety.
Hughes, who took over the club in November following the sacking of Peter Grant, admitted emotions were raw in the home dressing room afterwards but he is hoping to remain in charge next season.
“The first thing I’ll look at is myself," said the 57-year-old. "I’ll look at all the things, what have I done right and what have I done wrong? What could we have done better?
“I definitely want the chance to really take this club where it wants to go.
“It’s not going to be easy, I get that. But, once the dust settles, even as players, we need to come back and roll the sleeves up and be committed to getting the club back in the Championship."
Queen's, who had incoming manager Owen Coyle in the dug-out ahead of his official appointment in June, are now aiming to clinch a second successive promotion after winning League Two last season on the back of turning full-time.
John Potter, who has been in caretaker charge since January following the departure of Laurie Ellis, admitted he had mixed emotions as his hometown club, who he previously played for and managed, suffered the drop.
"My family were in the Dunfermline end today including my sons. It's disappointing for the club but I was here before when the club were in far worse state. They were in administration and didn't think they were going to be there. Yes, they've had a bad year, and that happens. It's disappointing. But it's a big club, a good club, and I've no doubt it will be back up to the Championship trying to push on again."
Both sides had their goalkeepers to thank in the first-half with Dunfermline stopper Jakub Stolarczyk brilliantly denying Luca Connell while Calum Ferrie somehow kept out an Ambrose effort.
The Pars upped the pressure but the match turned in the 58th minute when Ambrose lunged into a late challenge on Murray as he broke through on goal and referee Craig Napier brandished the red card for denying a goal-scoring opportunity.
And Queen's made the extra man count in the final minute when Murray slammed a Bob McHugh cut-back into the roof of the net to spark wild celebrations among the away fans, and dejection in the home end.
Potter added: “We defended really well as a team. The red card helps, but we’ve now got a big opportunity to get this club into the Championship.”