On the eve of last night's Europa League win against Maccabi Tel Aviv, McGinn penned a new deal to 2028.
And the Scotland midfielder says part of his decision-making was the potential of the current team.
“I think it's clear, we're all missing something that we've become so close to over the past few years,” said McGinn.
“What this squad has built, what we've created, a core group of really talented players who are willing to learn, improve and get on board with the club and the manager's ambitions.
“But each time we've been asked a further question, we've maybe just fallen a little bit short, which is grinding on us as players.
“We're all really close. I spend so much time with these boys that when we got to the Conference League semi-final and the FA Cup semi-final or the Champions League quarter-final. They hurt us a lot and they're still fresh in our memory.
“I know they affect the supporters. It affects everyone at the club and what it does is it makes us stronger for the next battle ahead and next attempt.
“We know what we need to do to cement our place in the club's history and each game we go into and each tournament we go into, we know we've got that to look forward to and hopefully at some stage that we can deliver on that.”