The result, paired with Coleraine's thrashing of league leaders Larne, means that the Glens are now just three points off the top of the Irish Premiership.

"You can't depend on other teams, we have to look after our own back yard," McCann told BBC Sport NI.

"We have spoken about it all week that we can't control what happens elsewhere but let's look after our own destiny and let's make teams work for it and do what we do. Whatever happens elsewhere, happens elsewhere.

"We have given ourselves a bit of a chance, we have to go at it again and it will be a very difficult game against a very good Dungannon side."

The Glens are now unbeaten in their past eight league games and were the 2-0 victors last time they travelled to Stangmore Park to face the Swifts.

Despite the important win, McCann also acknowledged that the side "weren't at our best" at Solitude.

"It is buoyant in the changing rooms," he continued.

"We probably felt that we left a bit out there, we weren't at our best and we probably didn't get the ball down as much as we should.

"At this stage of the season, every manager and team will tell you, it doesn't always work. It wasn't for the lack of trying. Sometimes when you try certain things, it doesn't work out.

"But we got our two goals, we got the three points and we'll move on and see what happens from here."