Barca announced on Thursday that Messi, a free agent since his contract expired in June, will not rejoin the club because of financial problems.
Speaking at a news conference on Friday, Laporta explained that the "disastrous" situation inherited from the previous board and LaLiga's rigid spending limits have made keeping Messi impossible.
Messi, 34, had reached an agreement to sign a new five-year contract at Camp Nou, extending his 21-year link with the club, and Laporta said the forward is devastated that it will not be possible.
"I don't want to generate false hope," Laporta said when asked whether the situation was retrievable. "During the course of negotiations, we've known of other offers for Messi. There was a time limit, for us and for [Messi's camp], because they need time. The leagues are starting.
"The negotiations with Messi have ended and it's brought us here without an agreement because of the salary limit. Leo wanted to stay, so he's not happy. We all wanted him to stay, but now, like us, he is facing the reality of what's happened. A reality that can't be changed."
Laporta said the only way to keep Messi would have been to accept the deal proposed by LaLiga this week, which would have seen 10% of the league's business sold to the investment fund CVC Capital Partners.
Weighing up the pros and cons of LaLiga's agreement with CVC, Laporta said no one is bigger than the club and that accepting the terms of the sale could have put the club at risk in the long term.
"It would not be in Barca's best interests," he continued. "We were going to receive some money, but we think that accepting it -- and affecting our [revenue from] television rights for the next 50 years -- is not something we can do [to keep Messi]. It's too risky. The club is above players, coaches and presidents."
LaLiga president Javier Tebas, who has been feuding with Laporta and Real Madrid president Florentino Perez over the creation of a European Super League, responded on Twitter.
"Not long ago, you were saying we [LaLiga] were broke," he wrote. "Now we're valued at €24.25 billion and there's access for [clubs] TO GROW, you're worried about the future income of a league you'd written off as dead.
"You know that the operation with CVC doesn't mortgage Barca's television rights for 50 years, what it does is give them more value for all clubs and that way you can MORTGAGE your BANKS and solve the debt problem. That's how you understood it a few hours ago."
CVC declined to comment but a source with knowledge of the sale said the reports were "completely wrong" and that the investment fund "continues to support the project."
Years of mismanagement have led Barca to this point where they are unable to register Messi, their record appearance holder and top goal scorer of all time. Laporta described the situation he has inherited from previous president Josep Maria Bartomeu as a "shipwreck."
He explained that with Messi, Barca's wage bill would be 110% of their revenue. Without Messi, it will still be 95% and they have work to do to get it down to the recommended level of 70%.
That made it impossible to register Messi with LaLiga for the upcoming season. The Spanish league set a spending limit for each club. Barca's was over €600m before the pandemic but fell to €347m last season. Further cuts are expected for the upcoming campaign.
Laporta said an internal audit has only just revealed the true severity of the club's financial perils, saying that it was "much worse than expected" and that Barca stand to register losses of €487m for the 2020-21 season.
After speaking to the first-team squad and coach Ronald Koeman on Friday at the training ground, the president said everyone must now pull together to lead Barca forward in what he described as "the post-Messi era."
He said: "There's sadness, but the players and Ronald are professionals. They have the chance now to show that with their talent they can lead Barca to success.
"It's time to take on the challenges we set ourselves and to try and win all the competitions we take part in. We demand professionalism and will give maximum support to the players and the coaches in pursuit of excellence."
Laporta said he was aware Messi has received several offers from other clubs but said he did not know if one of them was Paris Saint-Germain, which has emerged as the favourite to sign the Argentina international.
Despite the gravity of the financial situation, Laporta added that he believes new signings Memphis Depay, Sergio Aguero, Eric Garcia and Emerson Royal can be registered with LaLiga. He said they have all accepted lower salaries and that their situations weren't comparable to Messi's.
He also refused to rule out making further signings before the transfer window closes at the end of the month.