Accrington are one of the form teams in League Two, having extended their streak without defeat to 10 games.
McCartan scored an 89th minute free-kick to earn a 1-1 draw with Grimsby, and the 22-year-old is confident John Coleman's side can keep it going over the remaining eight fixtures.
"We don't fear anybody now," he said. "That's the mentality we have."
McCartan has been a major part of Stanley's improvement, having scored eight goals in his last 13 league matches to help them move up to 15th place.
They are yet to lose at home in 2017, but despite being safe from relegation and 10 points outside the play-offs, McCartan thinks they have plenty of motivation for the rest of the season.
He told BBC Radio Lancashire: "To not lose in 10 games is a great achievement, especially considering the position we were in six weeks ago. It shows how strong the lads are mentally, but we've got to keep it going.
"We can go unbeaten until the end of the season, 100 per cent. We've played most of the big boys. We've got Plymouth coming up, but we know we can beat them.
"That's our mentality. As the gaffer said after the Morecambe game, we're a team of winners now."
Forward Shay McCartan believes Accrington Stanley can extend their unbeaten run to the end of the season.