Romelu Lukaku believes José Mourinho has made him a better player after only 10 days working with the Manchester United manager.

The striker was signed last week, at the start of United’s US tour, for £75m from Everton. On Monday Lukaku scored his first goal, the winner in a 2-1 victory over Real Salt Lake at the Rio Tinto Stadium.

Just before that Mourinho had spoken to him on the touchline. Asked about this, Lukaku said: “He knows what I can bring to the team and he’s someone who is pushing me. I push myself too but he makes me a better player. I think I learned a lot from him in the last week and I’m glad I can work with him.

“I’m happy for my goal. There is still a lot of work to do; as a team we know we need to be much better. But I’m glad I’m here because you really see it’s a big club and that was the challenge I wanted.”

Regarding the move from Everton the 24-year-old said: “I am very happy now. This is the job I wanted. I have to make sure that I stay focused and have the same ambition I’ve always had. And just work hard – that’s the key to success.”

According to Phil Jones United’s squad are the strongest since the club last won the Premier League in 2012-13. Jones was a member of the Sir Alex Ferguson team who won a record 20th title and has since played under David Moyes, Louis van Gaal and Mourinho.

In the summer window Mourinho has added Lukaku and Benfica’s Victor Lindelof. Mourinho also hopes to sign Internazionale’s Ivan Perisic and a defensive midfielder, with Tottenham Hotspur’s Eric Dier a prime candidate.

In United’s first two games of their tour Mourinho has fielded different XIs in the first and second halves and each has appeared as strong as the others. United’s win against Real Salt Lake followed a 5-2 victory over LA Galaxy.

“We’re definitely a lot stronger this year,” Jones said. “We’ve recruited well, big Rom up front is a threat, handful. Victor has come in and looks like he’s been here for five years now. We’re positive and looking forward to it.

“There is strength in depth and that’s what we need. That’s what the manager thought we needed. He’s recruited well, we’re all working well and gelling well and looking forward to the start of the season but we’ve got some big games first.”

Last season United won two trophies, the League Cup and the Europa League, the latter ensuring a place in the Champions League despite finishing sixth in the Premier League. “I think slowly but surely we’re getting the winning mentality back,” Jones said. “It’s taken time but I think we are getting there now. Hopefully this season every time another team steps out at Old Trafford they know they are in for a tough time. I think we have seen that last season, albeit we drew too many at home. But we will put that right this season and we are looking forward to it.

“Definitely that has given us the foundation to try and win the title again. That’s what we need to do this season. Last season was disappointing in the league but we won the Europa League so that wasn’t bad. This year we definitely have to start challenging for the title. There’s no question about it but I think we can definitely do it with this squad.”

Jones added: “Whoever I’ve played under – Ferguson, Moyes, Louis van Gaal, Mourinho – if I’ve been fit then the majority of the time I’ve played. If there’s competition from other players, there’s competition. There are some terrific defenders at the club. That’s the way it should be as well. You want to test yourself against the best and with the best and that’s what we’ve got.”