Malaga, who earned only their second tilt at European football after finishing a club-record fourth in La Liga last season, play host to Zenit St Petersburg on Tuesday on the back of a run of four wins and two draws from their six competitive fixtures so far this campaign.
That has come despite the backdrop of the Spanish club's well-publicised financial problems and Pellegrini has urged his players to carry on what they have been doing.
"The most crucial thing we can do tomorrow is to play exactly like we have been doing," he said.
"The excitement and euphoria surrounding this game is felt by all the fans and the entire city.
This is the first time we've played in the Champions League, and the team is completely focused on this match.
"We need to beat Zenit tomorrow, and we're capable of it at home."
The other teams in Group C are seven-time European champions AC Milan and Anderlecht.
Milan and Zenit are considered favourites to top the group, with Malaga just behind, but Pellegrini insists Anderlecht should not be discounted, using the success of his former club Villarreal as an example.
"I think we also need to be careful of Anderlecht, they didn't qualify just to make up the numbers. These are three very difficult teams, as is the case in all the groups," Pellegrini said today.
"Some have bigger names than others, perhaps some have more potential or in a good moment, like Zenit - who have been Russian League champions twice, and really strengthened their squad.
"Thinking there is perhaps an easier team to beat than the rest in our group is the worst mistake we can make.
"Nobody bet on Villarreal and we got to the semi-finals and quarter-finals."
Zenit head to Spain in mixed form having picked up just four points from their last four league games, with their most recent result seeing them lose 2-0 at home to Terek Grozny on Friday.
Zenit coach Luciano Spalletti gave big-money summer signings Hulk and Axel Witsel their competitive debuts in that match, along with Renat Yanbaev.
Witsel is unavailable though due to a hamstring injury while Yanbaev is not registered.