The then Celtic defender only had a handful of caps prior to taking to the Wembley turf at the age of 31 – but he still feels aggrieved that Scotland left the iconic stadium empty-handed.
"I missed the first game with Holland and Craig Brown pulled me aside and told me I would play against England at Wembley,” the former Dundee and Hearts full-back recalled.
"That was amazing and it meant I could prepare for that game. I think we deserved something from the game and if Uri Geller hadn’t moved the ball we would have got something.”
Scotland’s participation in this summer’s delayed Euro 2020 tournament is the first time the country has qualified for the European tournament since 1998, and the 56-year-old has fond memories of the competition.
"Euro 96 was special – England at Wembley is every schoolboy’s dream,” he added.
“If you think about the game, we started really well and then they got a foothold with the goal. When we got the penalty we looked really strong at that point and if we had scored I think we would have beaten them.
“But we missed and then Paul Gascoigne comes up with a bit of magic and sometimes you have to hold your hands up and say there’s nothing you can do about it.
“If you win it is the best game ever, but when you lose it is so disappointing. I still have plenty of special memories of going to Wembley and playing England.”
McKinlay is also cheered by the news that at least some supporters will be allowed into stadia, after 12 months of games being played behind closed doors. A little over 12,000 spectators will be present for Scotland’s two matches at Hampden.
“It was a great spectacle [in 1996] and it is great that a certain number of fans will be at the tournament. Getting back to tournaments is a great boost for the country.”
McKinlay, who joined Celtic in 1994 after nearly seven years with Hearts, was 30 before he earned his first cap in a European qualifier against Greece in 1995 at Hampden.
A catalogue of injuries forced a number of changes.
"I was a rookie but I was 30, so I was the oldest rookie in town,” he said. "From there I never looked back, and ended up getting 22 caps.”
After McKinlay earned his first cap against the Greeks, he was selected for the Euro 96 squad and again for the 1998 World Cup in France, during which he made substitute appearances against Brazil and Morocco.
He is hopeful that another defender with Celtic connections in Kieran Tierney will be able to shine for Scotland on the big stage.
"Tierney has been magnificent. At Celtic he was an out-and-out winner and he goes to Arsenal and wins the FA Cup. Not many have done that.
"He is a fantastic player who will go from strength to strength and this is another achievement, helping Scotland to a major finals.
“Teams will be looking at him as Arsenal aren’t really firing right now. But he will just be focused on Scotland.”