The Argentine superstar's 21-year stay with the LaLiga giants came to an end after 'financial and structural obstacles' prevented him from signing a new deal.
The four-time Champions League winner subsequently joined PSG on a free transfer, but has so far struggled to live up to his billing under Mauricio Pochettino in Paris.
Barca president Laporta suggested Messi, now 34, could have stayed at Camp Nou if he had been willing to go without a weekly salary.
When quizzed on his transfer to the Ligue 1 side, Laporta told RAC1 in October: "I hoped Messi would do a U-turn and he would say he would play for free.
"I would have liked that and I would have been all for it. It is my understanding La Liga would have accepted it. But we cannot ask a player of Messi's stature to do this."
Messi, however, has now hit back at those claims, which he believes made him out to look undutiful to his former club.
"The truth is, as I explained when I left, I did everything possible to stay," Messi told Sport.
"Never at any moment did they ask me to play for free. They asked me to reduce my salary by 50% and I did it without any problem. We were willing to help the club more. My desire and that of my family was to stay in Barcelona.
"No one asked me to play for free, but at the same time the president's words were inappropriate. It hurt because I don't think there was any need to say that.
"It's like taking the ball from you and not accepting the responsibility or taking charge of things. That makes people think and generates doubts that I don't think I deserve."
Messi joined Barcelona's famed La Masia academy as a 13-year-old before becoming the club's greatest ever-player and all-time top goalscorer.
Laporta was re-elected in March with hopes that he was most likely to keep hold of their talisman.
Messi admitted that he has not made contact with Laporta since leaving the club last summer but hopes he can return to the club where he made his name in some capacity in the future.
"I always said that I would love to help the club and be useful. I would love to be a sporting director at some point. I don't know if it will be in Barcelona or not, or if it will be something else," added the PSG forward.
"If there's the chance, I would like to go back and contribute what I can because it's the club I love and I would love them to keep doing well, growing and being one of the best in the world."