Laporta claimed he would've liked Messi to return even if it meant the Argetine star would play for free due to the club's financial crisis.
Instead, Messi opted to join Ligue 1 giants Paris Saint-Germain on a free transfer and is already one of the club's highest-earning players.
"The truth is that, as I explained on my way out, I did everything possible to stay, never at any time was I asked to play for free," Messi told Sport.
"I was asked to cut my salary by 50 per cent and I did it without any problem. We were in a position to help the club more. The desire of me and my family was to stay in Barcelona.
"Nobody asked me to play for free but at the same time, it seems to me that the words said by the president are out of place. They hurt me because I think he doesn't need to say that, it's like getting the ball off you and not assuming its consequences, or taking charge of things.
"This makes people think or generates a type of doubt that I think I do not deserve."