Boro are now 11th in the Championship table after a run of five defeats in their last six games and were booed by the Riverside fans at half-time and full-time on Saturday.
Carrick said he was “gutted” for his players and admitted confidence has taken a hit after the bruising run of setbacks.
But the under-fire boss insists he can turn it around.
“I fully believe we can get out of this,” he said.
“There’s a big different between a confidence hit in a tough moment and then the belief of what you’re capable of, and that it can turn. We’ve all seen it. Things can turn, but when you’re in it, you’re really in it.
“At the moment, we are in it, and there is no getting away from that. We’ve got to accept that. The boys will pull together, we’ll all pull together and we’ll find a way through it. But when you’re in it, it’s not a nice place to be. We have to stick together.
“100% we’ll get through it. What gives me that belief? We’ve got really good players and we’re a fantastic team. We’re just having a bad spell. A lot of teams have bad spells. You see teams throughout the country having bad spells. We don’t want to have them, but it’s part of the sport unfortunately. I don’t like it, but it doesn’t mean we can’t change it.”
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Watford had won just one of their last 10 games prior to their trip to Boro but secured all three points thanks to Moussa Sissoko’s header five minutes before half-time.
Carrick said: “I’m gutted for the players. I feel for them so much. They were wanting and trying to do the right things, but you can see that confidence is low.
“Confidence is what enables you to perform at a top level and we’re finding that at the moment. It’s understandable when things are going against you, so to see them fighting and pushing and trying to do the right things – we just couldn’t quite find that goal towards the end – that was my main feeling, just feeling for the boys right now.
“It’s easy to criticise the boys and criticise me, I understand that. But in terms of the players, they’re giving absolutely everything at the moment and it’s just not happening.
“That ultimately stops with me. I’ve got to find a way to guide them and help them through it. It doesn’t take much to swing it the other way, but when it’s going against you like this, it really goes against you. I do feel for them.”
