United led 2-0 after second-half goals by Juan Mata and Marouane Fellaini in the first leg at Old Trafford, but Tom Huddlestone's penalty got Hull back in the tie before half-time.
Paul Pogba levelled for United and Oumar Niasse's late goal proved irrelevant as United progressed 3-2 on aggregate, although it sealed a third straight home victory for Hull, leaving Silva dissatisfied.
"It was a good win but not enough for our goal," Silva said. "It is important to win the game but the result in the first leg caused problems for us.
"It was a good performance again, a good attitude and we controlled the game in large periods against a big team.
"It is impossible at this moment to feel really happy. The goal we conceded is not a normal goal, we lost control at the vital moment. It is important that we won the game.
"We have won three games in a row at home and when I arrived we had won once in two months. I congratulated the players in the dressing room."
Hull have sold Jake Livermore to West Brom and Robert Snodgrass is expected to leave the club imminently, with Silva aiming to be able to add to his squad before Tuesday's transfer deadline.
"I hope to improve the squad with three or four players. We need them," Silva said.
"We have 15 or 16 players, it's not normal at this level."