The event at Glasgow Green took place before the introduction of vaccine passports, which will be needed for entry to nightclubs and larger events from October 1 after the Scottish Parliament backed the plans last week.
Up to 50,000 music fans a day attended the three-day TRNSMT festival from September 10-12 and had to provide proof of a negative NHS Covid-19 lateral flow test to be allowed in.
Professor Leitch said TRNSMT checked every single person and that the process appeared to have gone "very smoothly", but that talks are under way about the logistics of checking vaccine passports at events like football matches.
Scottish Professional Football League (SPFL) chief executive Neil Doncaster has said the organisation is "concerned" about the practicalities of delivering the scheme and said spot-checking is the only way it can be done.
Professor Leitch said that spot-checks are "not a ridiculous idea" and that they are one option, while staggered entry is another.
He told BBC Good Morning Scotland: "TRNSMT tested every single person and they checked every single person, we had some meetings earlier in the week to debrief about how that had gone and it had gone very smoothly, now that is relatively simple visual check of an app or an email or a test, so it's not impossible but we do need to work out what Neil's saying,
"Sixty-thousand people at Hampden all arriving at once, that does create some logistical difficulties, so we've had conversations with those sectors pretty much every day since this came out, colleagues of mine, and we're working on what the final recommendations will be for ministers to then decide.
"Spot-checks is not a ridiculous idea but we just need to get the balance right don't we, between checking 60,000 and checking six, so somewhere in there is probably a sweet spot."
He said that authorities do not want to make attending football or rugby matches a chore, but that with more than 4,000 cases a day and 30 deaths reported on Wednesday such measures are necessary.
Professor Leitch said: "Inconvenience is one of the things we've had for 18 months and inconvenience is going to continue until we can get on top of this wave."
He also said there were no signs the music festival or the return of students to further education has led to a big rise in cases.
He said: "We've got no signs of TRNSMT causing us big levels of infection and I would have expected that to start to come through by now, although it is early days.
"Further education has been back for a few weeks now, again no big spike from them."
The Scottish Parliament voted last week to bring vaccine passports in for nightclubs and larger events from October 1.
This includes outdoor events of more than 10,000, which will cover football matches involving larger clubs.