Emotions ran high after David Marshall's heroic penalty save from Aleksander Mitrovic booked Scotland's place in next summer's delayed Euro 2020 finals having had qualification seemingly snatched from their grasp in normal time by Serbia's last minute equaliser.
Scotland put that bodyblow behind them to emerge victorious in the shoot-out after a fraught extra-time period, and while Clarke managed to maintain his trademark imperturbability, he admitted some of his players had broken down after delivering a historic result for the nation.
Clarke said: "I'm actually remarkably calm. I thought I might have a little tear - I know a few of the boys are in tears - and that tells you how much it means.
"When Marsh saved the last penalty I had a little glint in my eye but I managed to keep my emotions under check. I might have a little cry when I get to my room later on."
Scotland produced one of their best away performances in years when it mattered and deservedly took the lead on 53 minutes through a sublime finish from Ryan Christie.
The visitors had one foot in the finals until Luka Jovic equalised with a 90th minute header from a corner kick to break Scottish hearts.
The Serbs dominated extra-time but Scotland hung on for the shoot-out where strikes from Leigh Griffiths, Calum McGregor, Scott McTominay, Ollie McBurnie and Kenny McLean ensured a 100 per cent success rate for the Scots for the second shoot-out running following the semi-final win over Israel last month.
Serbia had converted all four of their attempts until Marshall made the block from Mitrovic to spark wild celebrations.
"Normally we fall at the final hurdle or we have the glorious failure," Clarke added.
"It's a magnificent night for everybody in Scotland. We said we'd try to put a smile back on (the fans) faces, and I hope they enjoyed the moment as much as we did in Belgrade and they can smile tomorrow."
The win also extended Scotland's unbeaten run under Clarke to nine matches - the longest sequence since 1976.
"Maybe a couple of months ago people still doubted us a little bit but we've shown that we've been building character in the squad and a fantastic backroom staff for me to work with,” Clarke told Sky Sports.
"We've been positive for a long time. We've taken a little while to get everybody onside with us but I think after last month people started to believe and this time we didn't let them down. The whole nation can be proud but nobody can be prouder than the players because they were magnificent.
Clarke becomes the first manager since Craig Brown, who guided Scotland to the World Cup in France in 1998, to lead the national team to a major tournament.
"I have to thank the board at the Scottish FA for showing their faith in me and thankfully I've managed to deliver for them,” he added. “It's been a difficult time for the country and financially for the Scottish FA this is a big step forward so I'm delighted for them that the players managed to produce.”