The Andalusians, who face a two-leg Champions League play-off against Greek side Panathinaikos later this month, have seen Spain playmaker Santi Cazorla and Venezuela striker Salomon Rondon sold on to Arsenal and Rubin Kazan in the last week.
Malaga confirmed on Friday that Netherlands defender Joris Mathijsen was also leaving to join Feyenoord but Pellegrini said he was determined to see them through to the group stage of Europe's elite club competition for the first time.
He criticised the club's owner, Sheikh Abdullah Bin Nassar Al-Thani, for not ensuring he and his players were paid on time and said the process of "internal restructuring" announced last week should have been launched much earlier.
"With regard to my situation here, it's very clear," the Chilean, a former Real Madrid coach, told a news conference.
"I'm staying here to help the team as much as possible through these tough times."
"It's just unfortunate that everything has been left until the last minute.
"Teams have from May 13 to undergo the restructuring process and plan everything as well as possible but now there's hardly any time left, as everything was on hold.
"However, we have no intention of turning our back on the club. We know it's not going to be easy, but we'll be fighting as hard we can to qualify."
DISGRUNTLED PLAYERS
Pellegrini said he had persuaded some of the players who were disgruntled about delays in wage payments not to launch legal action against the club.
"Every player has performed fantastically well during the pre-season, but I don't think it's acceptable that they've had to wait this long for payment. These problems could be resolved in five minutes," he added.
"As soon as the situation is sorted out with the players, then I'll stop worrying.
"I feel responsible that some of the team who didn't make an official complaint did so because of me.
"We'll analyse the future as soon as these problems are resolved, but changes definitely need to be made.
"Teams, players and whatever else the future holds will be decided at the right moment, but now isn't the time.
"The coaching team and the players are all completely focused on the Champions League and with the support of our fans we're excited about qualifying and looking ahead."
