The Red Devils conceded a late goal to draw against 10-man Tottenham in the Premier League on Saturday, leaving them with six points after six games, their worst tally at the same stage since 1986.
United visit Spanish side Atletico Madrid in the Champions League on Tuesday looking to improve on just one victory in their last six matches across all competitions.
"We definitely need to start strong tomorrow evening... we know what we're expecting tomorrow night, we'll be ready for it, the boys are ready for it," Carrick told reporters.
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"The way we responded (against Tottenham) in the second half in particular, I think you could see that, so that gives me a lot of faith that I had already in the boys, that they are hungry and eager to put things right."
Carrick said he could understand people saying the current situation was a "disaster" but that was not something he bought into.
"I understand when it's not going too well, there's a real kind of clamour, and a real feeling of 'it's a disaster' and 'it's all wrong' and 'everything needs to be changed'," he continued.
"I kind of get that, obviously, but that's not in our mindset, that's certainly not in my mindset.
"To achieve anything, really, you've got to be able to deal with things that are difficult and you've got to overcome things.
"That's part of it, I did it throughout my career just to be here... we're right there now in the middle of it, but I totally believe that we'll come through it."
Carrick confirmed Luke Shaw and Kobbie Mainoo had not travelled to Madrid after sustaining knocks in the draw with Tottenham.
The coach said he was not feeling outside pressure despite the team's poor start to the campaign and the corresponding scrutiny.
"I think there's our own expectation. We know what we want, what we're capable of doing as a team... and that comes from us," said Carrick.
"I certainly don't look outside or elsewhere at what it should look like.
"I've felt the ups and I've felt the downs, I don't feel a pressure from that at all. It's us wanting to succeed and we want to win, we want to be part of something successful, so that's the drive."