Promising Spain under-21 midfielder Isco scored either side of a goal by the club's new signing Javier Saviola as the La Liga side put the big-spending Russians to the sword at the Rosaleda and put themselves atop Group C.
"The team is working well, with a lot of internal motivation to make a project that has stumbled at times work and this is the best way to do it," Pellegrini told a news conference.
"The team put in a good performance against a great opponent who never gave up," added the Chilean. "The team is very focused on what it is doing."
Malaga qualified for Europe's elite club competition for the first time after finishing fourth last season following some hefty investment by owner Sheikh Abdullah Al-Thani, a member of the Qatar royal family.
Al-Thani appeared to scale back his ambitions for the Andalusian club this summer when they announced an "internal restructuring", sold several of their best players and brought in some cheaper replacements.
The uncertainty off the pitch does not appear to have affected the performance of the team, second in La Liga after four matches, basking in the glory of Tuesday's impressive debut in the Champions League group stage.
Argentine Saviola, who promised much early in his career but failed to live up to high expectations, was on the scoresheet for a second straight game after netting one and setting up a second in his first start for the club, a 3-1 La Liga win against Levante on Saturday.
"We proved that we can do things well in the Champions League," the 30-year-old told reporters.
"We knew that they typically play with intensity and that we had to make a good start.
"We were able to keep it up in the second half and everything worked out perfectly." (Reporting by Iain Rogers, editing by Amlan Chakraborty)