Mathieu played 32 La Liga games this season to help Valencia finish eighth and the defender has been linked with Barcelona and Bayern Munich, although the 30-year-old has denied contact with either club.
And Pizzi knows that Valencia must do everything to keep the left-back at the Mestalla.
"We need him and he is very happy here," Pizzi said.
"I think he has had the best form of his career this season and the best form of any defender in the Spanish league."
Pizzi confirmed that new owner Singaporean businessman Peter Lim is not ready to go on a transfer spree, meaning his must work within his means and recall on-loan players.
"All the loan players need to come back, then we'll decide what to do. In principle, they will all be at our disposal," he added.
"I cannot imagine that either Lim or anyone else would say, 'Here, here's a war chest and you can spend whatever it takes'.
"We need to be prudent because the formalities of the (club's) sale have still not gone through.
"There are issues with the bank and the foundation, so the sooner they are solved the better."
