Sunday's uninspiring 3-1 loss away to leaders Hearts left Glasgow giants Celtic eight points behind the Edinburgh club.
That defeat meant Celtic have dropped 10 points in their opening nine league outings and while the Hoops board and, more recently, manager Brendan Rodgers have born the brunt of fans' anger, skipper McGregor insisted: "The players always have to take responsibility, I've been saying it since day one.
"Even with the distraction of the (protests about the) board and (lack of) signings and everything else, I've been the one who has said 'no, no, no, the players have got to take responsibility'.
"The only guys who can fix it are the guys on the pitch. Yes, I understand, we're in a difficult moment, but the only people who are coming to save you is yourself."
He added: "We can't be looking at who is going to take the baton off you - we have to fix it. And what we have to do is learn quicker than we're learning at the minute or else we won't fix it, it's as simple as that.
"I've been saying it every week since the season started.
"I think the players understand the situation, but we need to turn that into action on the pitch.
"I see it on Thursday night (against Sturm Graz) when we were excellent. But we need to back it up three days later and then another three days later we've got to do the same."
Celtic last faced an eight-point deficit at the top of the table when arch-rivals Rangers, then under Steven Gerrard, won the Premiership title in the 2020/21 season.
McGregor, asked about the challenge of overhauling Hearts, replied: "They're eight points clear of us, and we're now the team that are chasing. If they're the guys at the top, then of course, we have to try to chase them."