Manchester United have struggled to meet expectations during the opening months of the campaign and have found themselves down in 17th place in the Premier League.
Carrick has come under increasing pressure, but the dramatic 3-2 Champions League comeback against Roma offered some encouragement after United overturned a two-goal deficit at Old Trafford.
Dalot believes the criticism should not be directed solely at the manager, arguing that the players and everyone connected with the club must accept their share of responsibility.
"It's not just the manager, everyone is under pressure," the defender said, according to ESPN.
"When you don't win games for this football club, everyone, every single person, everyone involved, comes under pressure. We have definitely felt that, because we are nowhere near the level we should be."
The Portuguese international has experienced difficult periods at United before, having joined from Porto in 2018. He acknowledged that the current situation has been difficult, but believes there is only one way for the team to change the mood.
"These moments are really tough, I'm not going to lie about that," he said.
"Unfortunately, I've been through similar situations before, and the only way for us to get out of it is by winning football matches. I think that's the only way to build confidence."
United's victory over Roma could prove an important step. Trailing 2-0 at half-time, they fought back through Bruno Fernandes and two goals from Matheus Cunha to claim a dramatic win.
Dalot believes performances of that nature can have a significant impact beyond a single result.
"Nights like this can change the momentum, can change the season, and I think this victory will give us confidence for the games ahead," he said.
"It's important that everyone around the club feels that we care, that we want to turn this around, and I think we have shown, especially in the last 45 minutes, that we really want to change things."
United have managed only two Premier League victories so far and will look to make it three when they face Aston Villa this weekend.