Froome said in a video on his YouTube channel that he was on track to be in peak condition for the Tour despite poor results in the build-up.
He was not selected in the eight-rider squad and Sylvan Adams appeared to dismiss Froome's claims when speaking to Radio Cycling podcast.
"Absolutely not. How could we say we had value for money? We signed Chris to be the leader of our Tour de France team, and he's not even here," Adams said.
"This is not a PR exercise. Chris isn't a symbol, he isn't a PR tool, he's supposed to be our leader at the Tour de France and he's not even here, so no, I couldn't say he's value for money."
Froome joined the fledging team in 2021 and is widely reported to be on a salary of around $5million per year.
But he has struggled to regain the form that took him to four Tour victories with Ineos Grenadiers (formerly Team Sky) after a career-threatening crash at the 2019 Criterium du Dauphine.
He did ride in last year's Tour and finished third on the stage to Alpe d'Huez but failed to start stage 18 because of a COVID-19 test while sitting in 26th place overall.
"I respect his past accomplishments, but if you want to be on this year's Tour team or next year's Tour team, we don't care what you did seven years ago," Adams said.
"We gave him opportunities to ride in the Tour, like last year for example, when he hadn't really earned his spot, on the basis that Chris gets better in a three-week race."
Israel-Premier Tech have enjoyed a solid Tour with the standout result being Michael Woods' win on the Puy de Dome stage.
"These guys earned their spots and I feel good about the team we brought here," Adams said. "Chris I know was disappointed, but he understood the decision."