Marshall sent Scotland to a major tournament for the first time since 1998 when he saved Aleksandar Mitrovic's penalty in a shoot-out win in Belgrade.
The 35-year-old made his international debut in 2004 and has experienced disappointments and long spells out of the team - runs of three, four and five years without a cap.
The Derby goalkeeper's 40th appearance proved to be the sweetest as he sealed a place in next summer's European Championship finals, where Scotland will meet England, Croatia and Czech Republic, the latter pair at Hampden.
"It's almost a numb feeling, it's been so long," he said. "Obviously I am a certain age now that I can remember old tournaments. It's been so long and it's just massively emotional.
"I am just delighted to be there. It has probably not sunk in. You probably saw Ryan Christie was in tears and it just shows how much it means to the lads to get there.
"Obviously families are willing us on, fans who can't be here. Hopefully by next summer everybody can get the chance to go.
"The travelling fans over the years have just been incredible. So I'm so happy (and) just desperate that come tournament time the Covid situation is cleared up and the fans can go and enjoy it."
Scotland, typically, did it the hard way. Christie's strike had them leading and they looked in control until Serbia threw men forward in the final stages and Luka Jovic headed a 90th-minute equaliser.
Thousands of fans back in Scotland feared another near miss but their team followed up last month's semi-final win over Israel with another perfect set of penalties.
"I said to Callum McGregor, it's the best way to win but if we had lost it would have been gut-wrenching," Marshall said.
"But if you're going to do it, it's the best way. The lads scoring 10 out of 10 penalties under that pressure is just incredible.
"It's just such a relief to get there and enjoy the scenes in the dressing room afterwards, they were unbelievable. Just a lot of young lads enjoying themselves.
"At my age I can sit there and take it in because it's been a long, long time.
"The lads have been incredible, and I hope they enjoy it because it doesn't come round that often.
"Hopefully it can become more of the norm but it's just a mixture of guys who have been there, backroom staff who do so much for the players that goes unrecognised. The relief in that dressing room. And obviously the lads who just turn up as youngsters and go and qualify for tournaments as if it's normal.
"It's just so excited, so emotional."
Marshall did not immediately enjoy his penalty stop. The former Celtic goalkeeper was wary of celebrating too soon in case he was penalised for encroaching.
"Immediately after it was a delay because the ref had said don't celebrate if you save because there's a VAR check," he said. "I got the decision before the lads jumped on me thankfully.
"I just hoped and prayed that he wouldn't order a retake because the lads were on their way They didn't know it was being checked.
"But I did feel it was good. I had a tiny bit of doubt but the referee let us know pretty quickly.
"But when you have waited 22 years, what's another four or five seconds?"