The 26-year-old left back agreed a long-term contract with the Premier League club on Thursday, shortly before the January transfer window closed.
"Monreal's exit is a very sad moment for the team," Pellegrini told a news conference, ahead of the visit of Real Zaragoza in La Liga. "It deprives us of a very important player who performed to the highest standards.
"Unfortunately the reality of the club is what it is, and there is no way of hiding it. It was an option that came up at the last minute, and the club thought it was appropriate.
"I understand they have to try and balance the books, because the pressure is on us from all sides, and we have received punishments. It is a major loss to us in sporting terms."
Qatari-owned Malaga were also forced to sell players in the close season despite having earned a first shot at the Champions League.
Although the squad have been suffering delays in wage payments they have reached the last 16 of Europe's elite club competition where they take on Porto later this month.
European football's governing body UEFA have punished the Costa del Sol side for unpaid bills to staff, other teams and the tax authorities, as part of a crackdown on club finances.
Malaga have been given a future minimum one-season ban which would come into effect if they qualify for European competition again over the next four years, though the club have appealed the ruling to the Court of Arbitration for Sport.
On a more positive note for La Liga's fourth-placed side, Brazilian forward Julio Baptista returned to their squad to play Zaragoza after around 15 months on the sidelines with injuries.
The 31-year-old former Arsenal, Real Madrid and AS Roma player, known as "the beast", has missed most of last season and all of the current campaign with a string of problems.
"Baptista is an important figure to have back in the team," Chilean Pellegrini said.
"He is a player who was unlucky to have a very long injury layoff, and now we hope he is completely recovered."