Cameroon international Eto'o moved from European champions Barcelona in a swap deal for Zlatan Ibrahimovic last month and will be out to impress in his first match for Inter against Serie A opposition.
"I really want the Italian Super Cup so much," the 28-year-old told La Gazzetta dello Sport. "Beating Lazio in Beijing would be the best way to pay back right away the faith I've felt in me.
"The club has done a lot for me, I have to pay it back on the field."
Inter coach Jose Mourinho was confident Eto'o, who scored 30 goals in the Spanish league last season, would quickly show his quality in the blue and black stripes of Inter.
"I believe he will play as motivated as every other Inter player in this match on Saturday," he told reporters in Beijing on Wednesday.
"We'll see how he does this week. What I'm sure of is he will definitely be on the pitch."
The Portuguese said all of his four new signings, including striker Diego Milito who scored 24 league goals for Genoa last year, were blending in well at the club.
Mourinho still wants to further strengthen his squad before the new campaign, particularly with a playmaker, but skipper Javier Zanetti is confident they can weather the loss of Ibrahimovic, Italy's top league scorer last year.
"I've never seen such a complete squad - we have alternatives for every role and system of play," he told Gazzetta.
New Lazio coach Davide Ballardini, charged with galvanising the club after a disappointing 10th place last season, also has a motivated new striker in Julio Cruz, who was released by Inter at the end of last season.
The experienced Argentine boosts an already impressive Lazio forward unit boasting Tommaso Rocchi, Pasquale Foggia and Cruz's compatriot Mauro Zarate.
"Nothing is ever certain in football," Rocchi told Gazzetta. "The fact that they are favourites is an advantage for us - we play better when we are under pressure. Last season our most convincing performances were against big teams."
The traditional pre-season encounter brings sport back to the Bird's Nest for the first time since the end of the Paralympics last year, and a 69,000 sell-out is expected.
