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Unlike the UK's 80 per cent salary guarantee, Spain's furlough system only pays staff 70 per cent of their wages for the first six months and just 50 from the seventh month.
Spain is one of the hardest hit countries in Europe with 140,510 confirmed coronavirus cases and 13,798 deaths.
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The club captain, 32, was among the first-team players to release a statement confirming the squad would take the cut.
Messi and his team-mates insisted they would have taken the pay cut, regardless of extra pressure applied by the board.
In a statement, the players said: "Then there is the latest drama, concerning a pay cut to help the club tackle the loss of income associated with the coronavirus pandemic.
"It doesn't surprise us that the club wanted to put us back under the microscope and try to pressure us into doing something we were always going to do.
"If the agreement has been delayed in the last few days, it's simply because we were finding a formula to help the club and also our employees in such difficult times."
However, this is not the first time Messi has publicly criticised the Nou Camp chiefs this season.
In February, he hit out at ex-defender and director of football Eric Abidal over comments regarding some players' commitment and effort around the time of Ernesto Valverde's sacking.
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