The Qatari-owned Spanish club, who knocked out Panathinaikos in the play-offs, host Zenit St Petersburg in Group C on Tuesday in a clash between two of European football's nouveaux riches.
"The excitement and euphoria surrounding this game is felt by the fans and the entire city, and it's understandable" former Real Madrid boss Pellegrini told a news conference.
"This is the first time we've played in the Champions League, but the team is completely focused on the match.
"If we want to get a lot further in this competition, we need to keep working hard and stay focused."
Pellegrini's side finished fourth in La Liga last year and have notched three wins and a draw this term, despite an unsettling summer on the Costa del Sol.
"It isn't a group of three," the Chilean said. "We have to be wary of Anderlecht, they haven't been gifted a place.
"To think one team is easier than another is the worst mistake we could make. No one gave Villarreal a chance and we reached the semi-finals."
