The Armenian provided two assists in United’s emphatic 4-0 win over West Ham on Sunday.
United’s last title triumph came in Sir Alex Ferguson’s final season in 2013, since when they have finished seventh, fourth, fifth and sixth in the table.
But United look a different proposition this season, with Mkhitaryan confident they can take aim at winning the league.
“We made a good start to the season,” said Mkhitaryan. “Now we have to keep going.
“As a club, you’re going to have ups and downs. I think the last few years was a little bit down for the club but, since last year and this year, I hope it’s going to be up for the club.
“We’ll do our best to bring the club to the level it was at before. It’s always hard, but we’ll try to do our best.”
Romelu Lukaku scored twice on his Premier League debut for the Red Devils as they put the Hammers to the sword.
On United’s new No.9, Mkhitaryan said: “It’s his job to score goals. It doesn’t matter how you score. The important thing is to score goals. He is going to score goals and he is going to help us.”
Lukaku may have scored twice on his debut, but United’s most influential player was arguably another summer signing, Nemanja Matic, who joined from Chelsea for £35m rising to £40m.
Matic was pivotal to United’s win and Mkhitaryan echoed boss Mourinho by admitting he was surprised Chelsea let a player of his calibre leave to join a title rival.
“Actually I am [surprised],” said Mkhitaryan. “But I’m very happy that we’ve got him.”