“We know that we have to stay calm and follow the process and train well – and then, when you get the chance to play, it’s five hurdles to get over.
“The fact we have been there and been successful, we can draw on that, but it’s not the only thing that’s going to make us successful.
“You won’t just win it off experience alone; you have to earn the right to do everything you can over the next five games to hopefully be champions.
Martin O’Neill is in his second spell as interim manager this season after the departures of Brendan Rodgers and Wilfried Nancy.
As a result of that and Hearts at one stage being nine points ahead, Celtic’s board has suffered a fair amount of fan criticism.
“I see what we’ve overcome already this season in terms of a little bit of adversity and a change of manager twice,” McGregor said.
“We’ve fought back from where we were and I see enough signs that the team want to win and can do enough to win. I wouldn’t be doing my job properly if I didn’t think we have the edge.”
McGregor says O’Neill has done an “unbelievable job” in turning around Celtic’s turbulent season and would be happy for the veteran Northern Irishman to stay in the dugout beyond the summer.
“I don’t think anyone can underestimate how good a job he’s done,” McGregor said.
“He’s pulled the club back together when it was fractured, he’s overseen a run of really good results. Performances have been getting better all the time and that’s from a disjointed start point.
“It’s never been perfect, but the job is to win games and he’s shown that in spades – he’s getting a tune out of the players.
“If we do go on and be successful, and hopefully we can win the Scottish Cup as well, then what an amazing season and it states his credentials for the job moving forward. The players are fully behind him.”