After a 2-0 defeat to Czech Republic in their opening match, a goalless draw against England at Wembley last Friday had put Scotland in with a chance of reaching the knock-out phase of a major tournament for the first time in history.
A win over Croatia would have put them through, but despite Callum McGregor grabbing Scotland's first and only goal of the tournament with a first half equaliser, they were outclassed in the end by the World Cup runners-up of three years ago as goals from Nikola Vlašić, Luka Modric and Ivan Perisic sealed their place in the last 16.
"I'm just devastated we're not through, but extremely proud of the effort," McGinn said.
"We didn't get off to the best of starts [in the tournament] but tonight we came up against an excellent team and their experience at tournaments showed in the end.
"We did lose goals at poor times but I think the main thing we've got to do is use this experience to drive us onto more tournaments. The World Cup [in Qatar] is our aim now.
"You look around the dressing room we've got a good age group, determined guys and we feel as if we didn't do ourselves justice. But what we did do is create history in coming here, and we want this to be the start not the end."
The former Hibs man is now turning his attention back to the World Cup qualification campaign which resumes in early September with tough trips to Denmark and Austria either side of welcoming Moldova to Hampden.
"We need to learn from this experience," McGinn added. “We're not used to it, we can't get away from that, but we need to become a nation that is used to it. We need to become braver and better. We can improve of course we can. You saw tonight there's certainly areas we can improve. But we've got the talent. Not only that, we've got the talent coming through."