Dungannon assistant manager Terry McCrory said his side had missed the chance to put pressure on those above them in the race for a top six Danske Bank Premiership place.
The Swifts lost 3-2 at home to the team directly above them, Ballymena United.
Johnny McMurray, Tony Kane and Leroy Millar were on target as the Sky Blues won at Stangmore Park.
Daniel Hughes netted twice for Swifts who had Paul McElroy sent-off.
McCrory said: “It is disappointing because we felt it was an opportunity to get level on points with Ballymena, with both sides vying for that seventh place.
“It was a strange game because we feel we’ve put in a good shift and some good performances.
“We lost Grant Hutchinson to injury in the first half and that rocked us a bit.
“But we are disappointed with the goals we conceded.
“Ballymena are a strong side and it was always going to be very difficult.
“They lost the final against us a few weeks ago so were coming here with a point to prove.
“It’s a setback for us, but we’ll go again.”