The Scottish Communities League Cup semi-final defeat to 10-man Hearts on penalties was a body blow to a side which has surprised many this term by rocketing up the Clydesdale Bank Premier League to second spot.
That has put them firmly on course for a place in the Europa League next term, but the shootout reverse to John McGlynn's Gorgie men at Easter Road following a 1-1 draw will have dented their soaring confidence.
However, McKay - who passed up two gilt-edged chances to hand his side the initiative before the game went to a spot-kick decider - insists the disappointment will only fire them on to achieve the club's highest SPL finish and land a first assault on continental competition.
He said: "We just need to use the pain of this defeat as a spur to finish off the season on a high.
"Every player wants to play as high as they can and Europe is one of the biggest stages you can play at.
"We have got a lot of games from now until the end of the season and a lot of hard work to do. That starts on Wednesday against St Mirren. We will be going there looking for the win, to keep our second-place position and to put us one step closer to Europe."
Andrew Shinnie had put Inverness ahead just after half-time but new Jambos loan signing Michael Ngoo levelled for the Tynecastle side.
Hearts then had Scott Robinson dismissed for a two-footed lunge on Owain Tudur Jones but Caley Thistle could not press on and lost out when substitute Philip Roberts missed the decisive kick in the shootout.
McKay, though, was adamant that no-one was attaching any blame to the on-loan Arsenal man.
He said: "We have all put ourselves up there. We have all volunteered to go up and it could have happened to any of us. It's one of the worst things that can happen in football but Philip's a good lad and will get stronger from it."
The Highlanders now face two tricky away days as they travel to Paisley to take on St Mirren in the SPL on Wednesday before clashing with Kilmarnock at Rugby Park in the Scottish Cup three days later.
Boss Terry Butcher, though, has no worries about a hangover following their Easter Road woes.
He said: "We have had a right kick in the privates and we have to bounce back on Wednesday. Then we have another cup tie on Saturday, all away from home.
"We have to get back to what we do best and that's winning football games.
"But it's been a great run and a lot of players will learn a lot from the game. We have all learned a lot from it - myself and (assistant) Maurice (Malpas) and staff and the players.
"Our fans got behind us. It doesn't seem a lot - two, two and a half thousand - but it's 10 times what we normally get and they made a great amount of noise and we couldn't reward them with a final.
"We have got one cup to concern ourselves with and the league position is looking good too."
The former England captain added: "It's not nice to lose and it's not nice to lose on penalties - I should know all about that - but it's nice to know I've got a squad that can bounce back and bounce back well.
"Whenever we do have a setback we generally bounce back very well so I'm looking forward to that."