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With the club in more than £1.1 billion of debt, they were unable to register a two-year contract that Messi agreed because it did not meet La Liga's financial regulations.
There were rumours circulating that Barcelona had asked some of its senior pros for salary reductions so that they could keep their greatest ever player, and that Alba rejected the request.
However, he dismissed any talk of that being true in an interview following the 4-2 win over Real Sociedad at the Nou Camp on Sunday.
He feels he has been vilified by sections of the media.
"Apart from being the best ever, Leo was the one who understood me best, so imagine the efforts I would have made for him to stay," Alba told reporters, as per Goal.
"It's not true [that Messi left because of a pay cut the captains rejected]. The Messi stuff was separate from the captains, between he club and him.
"I can't control everything that's said, but I've been around. Nothing will surprise me. If 10 out of 10 news articles about Jordi Alba are negative, it's normal that people think badly. I can't stand being doubted.
"When the club talks with me, I am willing. I'm from here, spending my whole life in Barcelona. That my commitment is questioned hurts me a lot. As the president hasn't spoken specifically about this yet, I suppose he will speak and he'll tell the truth."
A day before the Sociedad win, Gerard Pique agreed a significant pay cut that allowed new signings Memphis Depay, Eric Garcia and Rey Manaj could be registered.
The 34-year-old scored the opening goal and afterwards, in a brilliant post-match interview, insisted that both Sergio Busquets and Alba would follow suit - explaining that him being the first to do was merely due to timing.
A frustrated Alba also confirmed that it was the case.
"My lawyers have spoken to the club. Pique's was concluded first simply because of the timing but the willingness of all the captains was always as it had to be," he added.
"The lies annoy me, they tire me. I can put up with a lot, but I suffer for my family and the things they have to hear."
On Monday, Barca president Joan Laporta said the club's situation was "very worrying" as he revealed debts have soared to £1.15 billion.
He put the blame on predecessor Josep Bartomeu and revealed salaries account for 103 per cent of the Blaugrana's total income.