The Spanish international, who made his debut in the Gunners' 1-0 win over Stoke City at the Emirates on Saturday, joined the club for a fee of around £8.5m on Thursday as cover for the injured Kieran Gibbs at left-back.
Despite wanting to keep the player, Pellegrini admits that the La Liga side's financial state meant that they had no choice but to let Monreal leave.
"Monreal's exit is a very sad moment for the team. It deprives us of a very important player who performed to the highest standards," said Pellegrini in a press conference.
"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."
The move came just six months after Arsenal bought Santi Cazorla from the Spanish outfit.