The Frenchman is expected to return to Juventus once his contract at Old Trafford expires at the end of the month.
In a new Amazon Prime documentary called 'The Pogumentary' - which is set to be released on Friday - the 29-year-old discusses his future with former agent Mino Raiola, who passed away in April.
In excerpts seen before the release, Pogba said: "My thought process is to show Manchester that they made a mistake in waiting to give me a contract.
"And to show other clubs that Manchester had made a mistake in not offering me a contract."
According to the documentary, United made two offers to keep the player at Old Trafford, while Raiola also held talks with both Barcelona and Paris Saint-Germain.
In the film, Pogba is seen asking his former agent whether United submitted a second offer in July 2021.
Raiola replied: "Yes. They absolutely want you to stay. For me, the offer doesn't reflect that. I told them, 'If you want him to stay, don't make that offer'.
"I will make them understand that if they really want you to stay and they want to build a project around you, this time they have to act differently and put the money on the table."
Pogba added: "They're bluffing. How can you tell a player you absolutely want him and offer him nothing? Never seen that."
The Frenchman first arrived in Manchester from Le Havre as a 16-year-old in 2009. He was allowed to leave the club on a free transfer in 2012 and went on to make a name for himself in the Serie A with Juventus.
After helping the club to four league titles, Pogba returned to Old Trafford for a then world record fee of £89milllion in August 2016. Two years later, the midfielder played a starring role as France won the 2018 World Cup in Russia.
Despite this, Pogba was rarely at his best for the Premier League side as his relationship with former manager Jose Mourinho soured.
The Frenchman's struggles at Old Trafford are summed up by Raiola in one clip from the documentary, when the Italian agent told Pogba: "We must try to make you feel as good as when you are with the French national team.
"You're different with them. You understand? You're another Pogba with the Manchester United team. It's not normal.
"With the France team, you're the real Pogba, the Pogba of Juventus, the Pogba that everyone loves. With Manchester, there's something blocking you."