While accepting he only remains in charge until the end of the season, the former United midfielder has hinted he'd be open to discuss a longer stay.
"Nothing's changed, to be honest," he said ahead of United's clash with Tottenham.
"I'm fully aware of the role I'm doing here and the responsibility I've got. We want to be successful, and I want the club to be successful beyond the end of the season - if that's me, if that's somebody else.
"At this stage, I can't control that and we'll see what happens, but it's certainly about trying to improve the team and making Manchester United stronger. Results over a short period of time don't change that.
"If they have changed there is something wrong. It can't be so knee-jerk whether it's really good or whether there's a few issues we need to solve."
Carrick added, "I'm loving what I'm doing. I'm here.
"I feel at home here, but I fully understand the situation, so I'm not getting too carried away."