The Tigers stormed into a first-half lead, via goals from Semi Ayaji and debutant Nobel Mendy, and United were unable to break through a resilient five-man defence from the hosts.
The final result means United have now lost to a newly promoted side in their opening game of a top-flight season for the first time in their history.
Captain Bruno Fernandes admitted United did not do enough to combat Hull's threat from set pieces and claimed the players slipped into bad habits from away games last season.
Carrick was frustrated at full-time, but looked to calm fan frustration over the result, by stating his confidence of things improving from this point onwards.
"Some of it was OK, but there's bits to improve on. It was never going to be perfect, but going behind and giving ourselves a lot to do makes it more difficult.
"It was a typical one of those games with a promoted team at home. You can't give them much, they've got a lot to hold on to.
"After that, we had moments and opportunities but we didn't have the spark to put the chances away or create more.
"We're bitterly disappointed with the result, but we won't let it knock us.
"When we keep getting stronger as a group, that'll come. Today's a game we can't ignore, we have a lot to learn from it - but we will.
"It doesn't change the direction the team or the club is going in. We stay calm and focus on next week."