The Portuguese's side have won their last eight successive games in all competitions after their FA Cup thrashing of Reading on Saturday and face a massive Premier League clash against arch-rivals Liverpool this coming weekend.
In spite of that, Mourinho says his side will approach this tie against the Tigers - who are bottom of the league but appointed his compatriot Marco Silva as the club's new manager earlier this week - with 100 per-cent focus and concentration.
Mourinho: Why not try and win it?
Mourinho told journalists: "Hull probably treat the semi-final as a big occasion for them. I don't know. For them, [maybe] it's more important the match that they have to play three days later in the Premier League.
"We play against Liverpool, which is a big match for us, but we want to be in the final so we are going to face this Hull match with everything we have and with all the power we have.
"We know that it's two legs but the second leg is away, so if you can in the first-leg, do something that gives you an advantage. We are going to try that.
"For big clubs, a competition is a competition. I was never good at choosing competitions.
"Many times in some of my clubs, you arrive and you have a very busy fixture list but you are in competitions to try to win, to try to do things.
"I always felt, the League Cup as a cup is not the FA Cup, but it's a cup. I won it twice in Cardiff, but when it moved to Wembley I think the meaning is even better. So why not try?
"It's a two-legged tie so you have even the chance, if you don't play well in one leg, you have another match to try.
"So we're going to try and I know Hull City's new manager is an intelligent guy who will organise his team well for sure. But we want to be there."
United boss keen to maintain winning ways with strongest line-up expected at Hull
The Red Devils boss guided his side to another victory in cup competition as Wayne Rooney's historic goals, in addition Anthony Martial's strike and a Marcus Rashford brace, ensured a comfortable 4-0 win over Reading in the FA Cup third round on Saturday.
Mourinho added: "To win it, we have to win three matches. Or not three because it's two legs, but win the semi-final and the final.
"We have Hull City and then [it would be] either Liverpool or Southampton in the final. It's not going to be easy but I think the fact that you are winning matches is good and you are not going to throw away an opportunity for that."
Speaking on Saturday on the team he's likely to field against Hull at Old Trafford, Mourinho continued: "I play with the players that didn't play today [against Reading]. Today I played with fresh players.
"I don't want to put things in first-team or second team, or first choice or second choice, today I played with fresh players - the players that didn't play against West Ham.
"The next match against Hull, I'm going to play again with fresh players, so it's easy to know our team. It's Zlatan [Ibrahimovic], it's [Paul] Pogba, it's [Ander] Herrera, it's [Antonio] Valencia. It's the guys who didn't play today."
Silva known in Portugal as one of the "good young coaches", says Mourinho
Mourinho also hailed Hull's new boss Silva and insisted that his time at the KCOM Stadium is a big opportunity for the 39-year-old, although added he only wishes him success after their two semi-finals.
Silva took charge of his first game as the Tigers' boss with a 2-0 win over Swansea City in the FA Cup thanks to late goals from Abel Hernandez and Josh Tymon, with the club earning their first clean sheet in 23 matches in all competitions in the process.
He said: "It's not easy to come to the Premier League when you are a foreign coach.
"I spoke with him yesterday [Friday] and he was right when he says that it's an opportunity for him to come to the Premier League and he knows he's going to face a different challenge.
"They are bottom of the league with I think 13 points, but it's a big opportunity for him. He's known in Portugal as one of the good young coaches.
"He went to Greece. In Greece, I think nobody knows what they do there. Nobody knows that he was champion, nobody knows what they do.
"Now he comes to the big one. It's a big opportunity for him, so I hope he loses these matches and wins every [other] one.
Mourinho, asked about Silva's career path and the qualities he will bring to the English top-flight, added: "His formation was good because he started from the lower teams. He wasn't given a top job immediately.
"He did well at a small club in Portugal. Then he goes to Sporting, one of the top three, and he won the cup and finished second in the league. Goes to Greece, he's champion with Olympiakos.
"For me, he's very stable in spite of a young guy. He's experienced, he's very stable, he's very mature. I look forward to another Portuguese, in this case one from a younger generation than myself, being in this league.
"I'd love him to do well, but we all know that in the Premier League when you're bottom of the league it's hard to jump. But he's going to try for sure."