The 41-year-old felt the quartet did not fit into the Blaugrana team for a variety of reasons, but the club feared a backlash from supporters if they had departed
The coach called time on his four-year spell in charge at Camp Nou in May, citing exhaustion and a need to recharge his batteries.
However, according to the representative, he could have remained in his post, but club president Sandro Rosell saw the quartet as untouchable.
"Guardiola announced his terms of renewal to Rosell. Among them was the sale of four players - Alves, Pique, Cesc and David Villa," Gallardo was quoted as saying by AS.
"Pep did not seem committed to Fabregas, Gerard and Dani, while the reasons for Villa leaving were sporting. He was especially disappointed in Cesc as a person, as he had refused to shake his hand when he signed.
"These players were regarded as untouchable, and the fans would not have accepted the sale."
Guardiola's successor, Tito Vilanova, has enjoyed an unbeaten league start with his side sat in first place, level on points with Atletico Madrid.