The Cherries ran riot at Old Trafford in a 3-0 win, brushing aside a Man Utd team without the dropped pair of captain Bruno Fernandes and forward Matheus Cunha.
Former Man Utd defender Gary Neville, on co-commentary duty for Sky Sports, said club bosses Omar Berrada and Jason Wilcox would soon make official the decision to sack Carrick which will be very unpopular with fans.
Neville said: “Those two are probably going to make a decision which will disgust Manchester United fans, but is probably necessary.”
Jamie Carragher added that Carrick must be sacked “tonight”, adding: “Carrick needs to be relieved of his duties – for the good of Michael Carrick.
“He’s emotional, he’s hurting, it’s not good for Manchester United and it’s not good for Michael Carrick.”
Carrick walked around the pitch applauding the supporters at the full-time whistle, which Neville suggested appeared to be a goodbye to the fans.
But Carrick insisted soon after that wasn’t the case, telling Sky Sports: "It wasn't [a farewell from me]. It was mixed emotions. I'm feeling for the players because they are going through a tough spell, some of it we can help, some of it the situation unravels and the boys are feeling it.
"Mixed emotions for the supporters to respond in that way and to have the connection with the supporters, in the moment we are in is mixed emotions and I need time to digest that. I appreciate their support.”
Asked if he expects to face talks over his job in the coming days, Carrick said: “The situation is where we are at. We haven’t had the performances or the results. It's a tough situation, there is no hiding from it.
“What's next, I really do not know. But I always do what's best for this football club and I don't change that now. I love what I do, I love the position I am in and I feel the responsibility, but we'll have to wait an see."
He added to BBC Sport: “See what happens. I'm not expecting anything. It's just digesting today - we knew it was an important day to try and get us moving forward and we haven't done that.
“For me it's just digesting that and the emotions at the end of the game is something I've not really had before.
"I've got the energy for sure - it means so much to me. You have games to focus on and gathering the players. The responsibility of doing that I enjoy that - I love it, it's what I'm here for."
Harry Maguire, who was captain for the day in the absence of Fernandes, believes the blame lies with the players.
He told Sky Sports: "At the moment we're not doing enough as players.
“Michael turned our season on its head last year and we played brilliant football and got brilliant results. This season we haven't performed well enough as individuals."