Man United took until the 56th minute to open the scoring against the Tigers, before Marouane Fellaini headed a late second to secure a 2-0 victory against a Hull team that impressed for long spells despite a number of injuries.
Mourinho has claimed that he "would have been happy with 1-0", but was pleased to add another ahead of the second leg at the KCOM Stadium on January 26.
"I was expecting a difficult match. I was not expecting to win by four or five. I would have been happy with 1-0, but two is better. We are not at Wembley, but the second goal is an important goal," Mourinho told Sky Sports News.
"I was a bit disappointed with the first half, we were a little bit sloppy and complicated things. We always wanted one more touch and gave Hull time to regroup. It was not our best first half and we had to do better.
"I now think about Sunday. I need to do better, the players need to do better and the stadium needs to do better."
Mourinho also said that he fully expects to have leading scorer Zlatan Ibrahimovic back from illness for Sunday's Premier League clash against Liverpool.