That result moved Newcastle to within a point of fourth-placed Tottenham and are only three points behind United in third, with the North East club having a far greater goal difference.
Eddie Howe’s team will welcome the Red Devils to St James’ Park next after the international break in what promises to be a huge scrap for a Champions League spot.
And Carrager believes Erik ten Hag’s team are in a big battle to secure a spot in the top four as he told Sky Sports: “That result pulls Manchester United into the pack, especially with Newcastle playing Manchester United next.
“Newcastle will have to get used to this. They’re going to be involved in European football, they’ll be expected to go further in cups.
“The thing that really impresses me is their running system. Forest went man to man and they couldn’t really cope with them.
“I love watching them. The big thing for Newcastle and Tottenham is the fact that Tottenham do have to go to United.
“The thing about Liverpool and Tottenham is it feels like there’s a little bit of unrest at both clubs. I don’t think you get that at Newcastle.
“Even when they don’t win a game it’s still a really good performance. I very rarely watch them and am not impressed. This break may actually be coming at a bad time for them.
He said: “United will be without Casemiro in the next four matches which will make a big difference and Newcastle are now in a position where they can make a good push.
‘This is the time to hit form, but there’s still a long way to go. Eddie Howe won’t be getting carried away, but he will feel more confident after the last few days. It’s a really tough run in for Newcastle.
“Chelsea, Tottenham Liverpool, other clubs have had disappointing seasons. What I like about Newcastle is it’s been a measured transition in the way they chose their manager and brought players in.
“There’s some pretty solid characters in that dressing room. They’ve got a great chance.
“I’m stunned as to where they are this season. I thought they would be seventh or eighth. Well done to Eddie Howe, well done to the players, and it looks like they’ve just turned a corner.
“Isak is on a roll. He’s really important to them. Callum Wilson is going to struggle to get into the team.”