"The team must run and fly on the field when they play against Saudi Arabia, they must show their true worth. If the preparations have been effective methodically, Russia must simply outrun their first opponent," Tarpishchev said.
He added that it was natural for the players to have "hardly dragged their feet" during their last two friendlies as the team should get their act together only by the time the tournament kicks offs.
Russia recently played two warm-up matches against Austria and Turkey, which they lost 1-0 and drew 1-1 respectively.
Tarpishchev also said that the system build by Russia head coach Stanislav Cherchesov was similar to the one he used when training tennis players and the Russian team should reach their best shape in their second match at the tournament against Egypt on June 19.
"The plan is very simple, if the team reach their best shape by the time they play Saudi Arabia, they'll be out of shape by the [time they reach] knockout stage. I think Cherchesov has planned the preparations in such a way so that the team should put up a fight in the knockout stage and squeeze into the quarter-finals," Tarpishchev said.
The host nation will face Saudi Arabia in the World Cup's opening match at Moscow's 81,000-seat Luzhniki Stadium on Thursday, before taking on Egypt and Uruguay in their other two Group A matches.
Russia will host its first-ever FIFA World Cup from June 14 to July 15, with the games set to be held in a total of 11 cities.