Liverpool boss Klopp counselled the player through a difficult time when they were at Borussia Dortmund in 2013.
Earlier this season, Mkhitaryan did not play in the league for 10 weeks and remembered Klopp's previous advice.
"I am thankful to Klopp. He worked on my personality and the psychological part," 28-year-old Mkhitaryan said.
The Armenian spent two seasons working under Klopp in Germany before the coach quit, later taking over at Liverpool in October 2015.
Within eight months, the playmaker was following his old boss to the Premier League, joining United for a reported £26.3m.
However, after being substituted at half-time during United's 2-1 home defeat by Manchester City on 10 September, he did not play in the Premier League again until 27 November.
"At Dortmund, I was very stressed after a few games when we were playing really bad," added Mkhitaryan, who has scored five times this season.
"Klopp showed me the way. He supported me and told me I had to keep my head up because good things were coming. He helped me to become a player."
The move to the Premier League was another step on a remarkable journey for Mkhitaryan, who speaks six languages - including English - and is the son of one of Armenia's most famous footballers.
Father Hamlet was also an Armenian international and one of the first players from the country to play outside of the old Soviet Union. He died of a brain tumour when Mkhitaryan was seven.
"He was my drive, my goal, my dream," he said. "I did not feel the true impact when he died but I knew that he was watching me from the sky. He has to be very proud."
Mkhitaryan is now one of the most famous - and most wealthy - Armenians in the world. But his background is unconventional in United's multi-national squad.
He comes from a country that had a five-year conflict with neighbours Azerbaijan between 1989 and 1994 over disputed territory and still does not have normal relations with Turkey due to the treatment it received under Ottoman rule in World War One.
So Mkhitaryan had to carry out a period of national service before he was allowed to move abroad, initially to Ukraine's Metalurh Donetsk, in 2009.
"It was very hard growing up in Armenia because at that time we had a lot of problems with our neighbours and we had war, so it was a bad situation," said Mkhitaryan, speaking at a Manchester United Foundation #SchoolsUnited event in Moss Side.
"Before I could leave and be a football player I had to go to the military. I did that when I was 20. After that I was allowed to change my club."
Manchester United midfielder Henrikh Mkhitaryan has thanked Jurgen Klopp for the advice that helped him through a tough start to his Old Trafford career.