The 40-year-old former Barcelona centre-back had been assistant to Rafael Benitez at Liverpool and Inter, but was given solitary charge of the Spanish club in May, and he is relishing the prospect.
"I feel privileged to be here at Valencia," he told Spanish newspaper AS. "I feel extremely lucky and I want to take this opportunity.
"The truth is, this is something completely different to what I have experienced in the past, but I am focused on the job and extremely happy."
The Argentine tactician also commented on compatriot and new signing Fernando Gago, who arrived at Mestalla earlier in July.
"I hope he can adapt quickly to the team, and that the team can get the best out of him," Pellegrino continued.
Valencia have recently been linked with Salomon Rondon of Malaga, Diego Costa of Atletico Madrid and Kevin Gameiro of PSG, but Pellegrino remained coy: "More signings? We will see."
Los Che host Real Madrid on the weekend of August 18 as the new Liga season gets underway.