Celtic fans flooded out of the stands after the Hoops scored the third goal in their 3-1 home win over Hearts on Saturday which clinched the Scottish Premiership title.
There was another Celtic pitch invasion when Martin O'Neill's side scored a late penalty winner at Motherwell and there is an ongoing investigation into unseemly scenes at the end of the Old Firm Scottish Cup tie at Ibrox in March, where fans from both sides came out of the stands following the penalty shoot-out win for the visitors.
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Scotland qualified for the World Cup finals for the first time since 1998 with the most dramatic 4-2 win over Denmark at Hampden Park last November, but Clarke noted that the fans stayed in their seats to celebrate.
He said: "That [Denmark game] just shows that you can enjoy yourself without going out on the pitch.
"There is no need for people to be on the pitch.
"The reputation of the Tartan Army and the Scottish fans is well known worldwide. They will go away, they will enjoy themselves.
"Even over the disappointment in Germany (2024 Euros) the Tartan Army were top supporters.
"They made a lot of friends in Germany and I'm sure they will make more friends over in the States.
"I think the international scene is separate from the domestic scene.
"So the feelgood factor is around the international team. We feel good about ourselves and feel good about the last qualifying campaign.
"That finished on a fantastic emotional high here at Hampden so we are good.
"The way the league season ended with the scenes on Saturday at Celtic Park was not good for Scottish football. It's a bad look that doesn't do anybody any favours.
"It's much better that people celebrate but stay where they should stay.
"People invading the pitch is not right because player safety is endangered. That is not correct - anywhere.
"On the pitch is the players' place of work. People should not go on the pitch, it's quite clear."
Clarke hopes his future will be settled before leaving for the USA.
Ahead of the Euro 2024 qualifying campaign, he signed a new deal with the Scottish FA that runs out this summer.
Clarke has overseen three major final qualifications with Scotland, including two European Championship appearances.
Clarke was asked if he thought his situation would be clarified before they flew out to the keenly-awaited tournament and he said: "Hopefully. That would be the plan.
"I am pretty sure it will be. But let's just talk about the squad, not me. I am not important today."
One person who will not be going to the World Cup is Oli McBurnie, again left out of Clarke's plans.
The 29-year-old striker won the last of his 16 caps five years ago and remains without a goal for his country.
Last month McBurnie, who has scored 18 times this season to help Hull City to the Championship play-off final, revealed he phoned Clarke to get an explanation about his continued international exile.
The Scotland boss said: "I thought that was a private conversation to be honest. He should not have gone to the media.
"I tend to stick with players I have had before. I trust them. They know what I expect from them and that is it."
Scotland's World Cup squad:
Goalkeepers: Craig Gordon (Hearts), Angus Gunn (Nottingham Forest), Liam Kelly (Rangers).
Defenders: Grant Hanley (Hibernian), Jack Hendry (Al Etiffaq), Aaron Hickey (Brentford), Dom Hyam (Wrexham), Scott McKenna (Dinamo Zagreb), Nathan Patterson (Everton), Anthony Ralston (Celtic), Andy Robertson (Liverpool), John Souttar (Rangers), Kieran Tierney (Celtic).
Midfielders: Ryan Christie (Bournemouth), Finlay Curtis (Kilmarnock), Lewis Ferguson (Bologna), Ben Gannon-Doak (Bournemouth), Billy Gilmour (Napoli), John McGinn (Aston Villa), Kenny McLean (Norwich), Scott McTominay (Napoli).
Forwards: Che Adams (Torino), Lyndon Dykes (Charlton Athletic), George Hirst (Ipswich), Lawrence Shankland (Hearts), Ross Stewart (Southampton).
Where do Scotland play and when?
If you're not planning to go out to North America, prepare for some late nights! Or should that be early mornings?!
Scotland's World Cup opener will be against Haiti in Boston on June 13 at 9pm local time - but that's 2am on June 14 UK time!
Scotland stay on in Boston to face Morocco on June 19 at 6pm local time - 11pm UK time. Then it's down to Miami to take on Brazil five days later, and that's another 11pm UK time kick-off.
For those of you heading out there - if you think Euro 2024 was a trip of a lifetime, well, this is going to be the trip of a lifetime.
The 2026 tournament will take place across 16 cities in three North American countries: the United States, Canada and Mexico.
