Winless in eight games in all competitions, the 20-time English champions slipped to within one point of the relegation zone after a damaging defeat at Old Trafford.
"It's a tough situation," Carrick told Sky Sports. "What is next? I don't know.
"I'll always do what's best for this football club. I've said it all along; I don't change that now. I love what I do. I love the responsibility, but we'll have to wait and see."
Asked in a post-match press conference if he expects to be sacked in the coming days, Carrick replied: "I totally understand the situation. I'm not expecting anything in particular, to be honest. I'm carrying on as normal. I love this place."
Despite a dismal run of results, the United fans largely supported the former midfielder as he made his way off the field at full-time before they turned on the club's players.

"I have mixed emotions to have that connection with the supporters in the moment we're in. I need time to digest that," added Carrick.
"I appreciate their support, but the situation is where it's at. We haven't been good enough."
Carrick's decision to drop captain Bruno Fernandes to the bench and not even introduce the Portuguese international as a substitute backfired.
Fernandes, last season's Premier League player of the year, had criticised Carrick's tactics after a 4-1 thrashing by Como on Wednesday.
Carrick said before the game that call was a "pure football" decision, but it was hard to believe Fernandes was not being punished as he was left on the bench for the entire match.
"There are always times in games when you are trying to change the course of the game and to make a difference," said Carrick as he swerved questions on Fernandes's absence. "Those were the decisions we made today."
Carrick was only appointed on a two-year deal in May after a successful caretaker spell in charge led United to third place in the Premier League last season.
However, he has been unable to arrest the club's steep decline since his former boss Alex Ferguson retired as manager in 2013.
United were outspent by many of their rivals in the transfer market as they added just three midfielders - Youri Tielemans, Andrey Santos and Carlos Baleba.
But Carrick said a lack of investment did not justify such a decline in results.
"Last season to finish third was a really good achievement in the circumstances," added Carrick.
"We understood where that left us, what was next, what needed to be done and how we needed to improve, and where we were at as a team and as a group at that stage.
"I definitely knew that we hadn't cracked it and there was a lot of work to be done, but that doesn't mean to say that it should have gone this way."
English Premier League
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