Messi, 34, accepted a salary reduction of 50% but Barca were still unable to register him with LaLiga due to their spending limit for the season being cut to €97 million, almost €300m less than last year.
Therefore, after over 20 years in Barcelona, Messi left for Paris Saint-Germain in August, signing an initial two-year deal with the French side.
"I didn't get angry with Messi, but you reach a moment where both parties see that it cannot be and there is disappointment on both sides," Laporta told RAC1. "I know he desperately wanted to stay but there was also a lot of pressure on him because of the offer he had.
"He already had the offer from PSG. Everyone knows he had a big offer. We knew from him that was the case."
LaLiga has a minimum wage for players of around €150,000-per-year plus inflation since 2016, but Laporta said he believes the Spanish league would have allowed Messi to play for nothing.
"I hoped until the last minute there would be a U-turn and he would say: 'I'll play for free,'" the president added. "I could have been convinced. I understand LaLiga would have accepted it, but we could not ask a player of Messi's quality to do that."
In a wide-ranging interview, Laporta also said the club could yet sign up to the LaLiga deal with CVC Capital Partners which cedes 10% of the league's income to the investment firm. Had Barca agreed it in the summer, it could have helped them keep Messi, but Laporta refused to sign it because he argued it puts the club's future at risk.
Barca's gross debt stands at close to €1.4 billion after registering losses of €481m for the 2020-21 campaign. Despite that, though, Laporta said "big signings" are possible moving forward.
"[It is possible] because we have assets that can generate revenue in the form of investment or credit," he stated. "What we don't want is to increase the deficit. We don't want more debt. We want fresh money or investment to tackle the club's needs and that includes [signing] new players."
He also explained why a move for former player Neymar, who signed a new contract with PSG earlier this year, failed to materialise.
"We didn't have the results of the due diligence process at the time and we thought we had more of a margin to work with than we did," Laporta said.
"We tried, but the information we received on Neymar was not true. They told us he wanted to leave PSG, that he wouldn't stay there, but in the end he accepted the renewal offer from them.
"It didn't disappoint me because that's how things go. It's good [that it didn't happen]. It would have generated revenue because he is a reference around the world, but it wouldn't have solved the situation we find ourselves in."
Meanwhile, Laporta once again backed manager Ronald Koeman, despite sources telling ESPN he was exploring replacements after a run of just one win in six games. Xavi Hernandez is one of the names on the table and Laporta confirmed he spoke with him this week.
"I have a good relationship with Xavi," he said. "I speak with him often because we're friends, the same with Pep [Guardiola] who I spoke to the other day. One of them I had as a player; the other as a coach.
"What we have right now is Koeman. We are proud that he's our coach and we have faith in him. We are focused on turning round the situation, which is not what we wanted. But the season has just started and we are getting injured players back.
"At no moment have I said he would not continue. He deserves to be shown a certain amount of confidence. As president you think about the best solution and I had to assess everything. And, after listening to people I trust, I reached the conclusion to act as I did with [Frank] Rijkaard and give him time."