Pellegrini has signed a three-year deal to become West Ham's new manager, and it is understood that the former Manchester City boss has become the highest-paid head coach in the club's history.
Gale, however, has claimed that Pellegrini's appointment will only be successful if the West Ham board hand the Argentine significant funds to improve the playing squad.
"I'll only be happy when West Ham release the funds to buy players because I think managers are only as good as the players that they're dealing with," Gale told Sky Sports News.
"I just hope this isn't a smokescreen by the West Ham board to sign a 'profile manager', so that they don't have to buy players.
"Okay, he's going to become the highest paid West Ham manager in history but there's lots of money in the West Ham coffers and they need to spend it as well."
Pellegrini has spent the last two years in the Chinese Super League with Hebei China Fortune.