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.
Their preparations were disrupted by cashflow problems and reports that Sheikh Abdullah Al-Thani, a member of the Qatar royal family, wanted to sell after only two years.
Spain midfielder Santi Cazorla was sold to Arsenal and Venezuela striker Salomon Rondon to Rubin Kazan, but the club made a swoop for a new clutch of players near transfer deadline day after a place in the Champions League group stage was achieved.
That included U.S defender Oguchi Onyewu, Paraguay striker Roque Santa Cruz and Argentine striker Javier Saviola, who netted one and set up a second in his first start, in the 3-1 win over Levante on Saturday.
Pellegrini led debutantes Villarreal to the Champions League semi-finals where they fell to Arsenal in 2006, and was keen to stress that while Zenit, Malaga and AC Milan were the eye-catching names in the group, Anderlecht should not be under-estimated.
"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."
