Hernandez scored 20 goals for the Champions in 2010/11 and he has no plans to be a one-season wonder.
The 23-year-old said in L'Equipe: "I am very happy that, as a squad, we won the English championship. This is a wonderful thing, especially after a title race so competitive. Chelsea, Arsenal and even Manchester City battled to the end, but we never doubted our strength.
"Our team has such soul and such spirit. Success is written into the DNA of this club. I'm at the best club in the world.
"Everything is done to succeed and win titles. There is only the Champions League defeat that sticks in the throat.
"Personally, I am extremely happy with my season, but I do not rest on my laurels. I want to do even better next season. I want to help this club to make history."
He admitted his goal tally had taken even him by surprise.
"Early in the season, I thought I would have limited playing time, or very limited," he said.
"At best, I thought my season would be coming off the bench late in games, trying to unlock a complicated situation.
"Basically, the aim for the season was essentially to adapt to the Premier League, especially physically. But gradually I got playing time, and I started to feel confident, scoring a few goals early in the season.
"Everything was so fast. I could not have hoped for it. I had a dream season."
Hernandez says his team's 2-1 win at Stoke on October 24 was when he really felt comfortable as a United player.
"There was a game that really made me realise that I could have an interesting season. It was the match against Stoke City in which I scored twice," he said.
"Throughout the match, I felt perfectly at ease in the game. I felt like I had been playing for Manchester United for 10 years!
"Thanks to my team-mates, I could express myself freely on the pitch. I think it was the pivotal game in my season. I will remember it all my life."