The Jambos had the Swiss champions on the ropes at Tynecastle before Jorge Grant’s sending off early in the second half took the sting out of their bid to overturn a 2-1 first-leg deficit in their Europa League play-off.
The Jambos parachute into the Conference League, where they were pitted alongside Serie A outfit Fiorentina, Turkish side Istanbul Basaksehir and Latvian club RFS in Friday’s group-stage draw.
“It was a good occasion, the fans got right behind us from the start and players fed off that energy,” said McKay. “You could see that in the first-half performance especially.
“We were brilliant, it’s probably one of the best performances we’ve had.
“Going into the next set of European fixtures, it gives us real belief that we can compete at that level, create chances and do really well.”
It was confirmed on Saturday morning that Hearts would kick off their Conference League campaign at home to the Turks on September 8, with the glamour double-header against Fiorentina taking place over back-to-back weeks in October.
Robbie Neilson’s side return to cinch Premiership action on Sunday when they host St Johnstone.
Influential defender Stephen Kingsley faces a fitness check after a hamstring issue which made him “touch and go” for Thursday’s game forced him to go off in the closing stages. Toby Sibbick and Alex Cochrane are suspended.
Meanwhile, Callum Davidson is hoping Hearts’ European exertions can help St Johnstone cause “a little upset” at Tynecastle.
The Saints boss has been impressed with the sustained improvement his Jambos counterpart Robbie Neilson has overseen at the Edinburgh club over the past couple of years.
However, he intends to try to capitalise on any physical or mental fatigue in the Hearts ranks after their agonising Europa League play-off defeat at the hands of FC Zurich on Thursday.
“Robbie’s done a fantastic job,” said Davidson. “I really like the way they play football. They’ve got a lot of players with good individual ability and as a collective they’re really good.
“All credit to Robbie and his backroom team. It will be a really tough game. We’ll make sure we’re organised and hard to play against but we need to make sure we pose a threat to them going forward and hopefully we can cause a little upset.
“It’s a tough time when you have a game after playing in Europe on the Thursday and hopefully we can take advantage of that.”
The Jambos are likely to make changes to freshen things up, but Davidson insists Saints will be prepared for whatever team and formation Hearts send out.
“Robbie plays a couple of different formations so we’ll plan for those and make sure we’re ready for whatever comes our way,” he said. “We’ve got to make sure we do something a little bit different to try and catch them with a surprise too.”