Michael Carrick's team were undone by first-half goals from Semi Ayaji and debutant Nobel Mendy and they failed to react after the restart.
Hull's delight at full-time was matched by pragmatism from Carrick, who admitted his side did not do enough to start the season with three points, but insisted the result will not rock his players.
Captain Bruno Fernandes followed a similar message in his post match interview as the Portugal international admitted the visitors should have expected Hull's approach with more action.
"We know in the Premier League these types of away grounds are difficult to play at. You need to match their intensity and aggression. The two set pieces ended up costing us the game today.
"Same mistakes as we did last season, every away game we give too much of the ball to them.
"In the first 20 minutes, the goalkeeper was the one with the most touches.
"We need to press more, be more aggressive, and then again we need to work on set plays and not concede these type of goals.
"We knew before the game set-pieces would be a big part of their game. They played all pre-season with a back four but had a five against us for some height, for these moments.
"The most frustrating thing is that we lost the game.
"We understand the fans frustration, every season at the start we want to compete and win every game, but we need the fans on our side, and to believe in ourselves."
Up next for United is a home clash with another promoted team - against Ipswich Town on August 30 - as Hull head to Coventry City the day before.