"Cup competitions are special because it is a slightly different feeling".
Ibrahimovic's one-year deal at Old Trafford expired in June and was not extended following the injury.
Having added Romelu Lukaku, Victor Lindelof and Nemanja Matic to his squad, Mourinho is hoping United make at least one more signing before the window closes, with Gareth Bale, Ivan Perisic and Danny Rose among those linked with a move.
"In my other clubs what I had was more players scoring goals", he said.
"If we cannot strengthen the team in these areas we have players that we can trust". Our levels of confidence and knowledge are higher so I am happy to start the season. "Hopefully this season we will be right up there challenging". Step by step, we're going to fight.
United will be without Luke Shaw as they defender continues to recover from a foot injury while Ashley Young and Marcos Rojo are also long-term absentees. "Last season, two of them were not in Europe", Mourinho said.
The Red Devils finished in sixth place in the Premier League table last term.
His first season at United was a year of building - and now he is ready to get to the top again. "I have to try to win every match".
"I am happy with the effort the club did and that the club managed to do 75 percent of the work before the Premier League starts and until August 31. I'm on fire! But I will behave on the touchline, even if goals are offside".
While Mourinho has welcomed the new signings, he argues that of greater significance is the fact his team will not have their domestic fixture list disrupted by the Europa League this season.
The Hammers finished 11th in the Premier League past year, as they settled into their first campaign at the London Stadium, recovering well after a very shaky start at the new ground. But there are not many like that, just a couple. Yes, I thought that.
"It's not just for his qualities but my relationship with him".
He has trained with the club during his rehabilitation, though, and Mourinho has made clear he still believes the forward can do a job for him. He's not somebody who needs to learn all about the Premier League. He's a player who gives me what I like, which is consistency.
"I don't think I am in a position to be moaning and crying".
Asked if Manchester United was his team now, he didn't hesitate to agree.
'I'm not going to lie, this is a big week. That is normal, but that is not enough.
However, the United manager is confident that his team can improve on that, having had a good pre-season and are well prepared.