The Mexican legend criticized El Tri's treatment of the Real Sociedad forward, saying certain issues "aren't being dealt with in the correct manner."
"Carlos Vela took the decision for dignity and for pride," Sanchez said on beIN Sports' "The Locker Room." "Carlos Vela hasn't said no to his country, he's said no to some issues that aren't being dealt with in the correct manner."
Real Sociedad's Vela met with Mexico coach Miguel Herrera on Monday, but the two couldn't clear the path to the player's return to the national team setup, with Vela stating in an open letter that he isn't 100 percent mentally ready and that it wouldn't be fair to take the place of someone who has been through the qualifying process.
Sanchez, however, doesn't seem to believe that reasoning and said Vela is "hurt by the treatment that (the federation) gave him."
The former striker was referring in part to the 2010 incident when Vela was suspended for six months from El Tri after an alleged party in a Monterrey hotel.
"Carlos Vela is saying no to the bad treatment, bad management and the poor public display about the indiscipline," Sanchez added.
The ex-Real Madrid striker has been a ferocious critic in recent times of the Mexican soccer federation and indicated he will be speaking to Vela, whom he described as Mexico's best current player.