Parrott started all four of Ireland’s games in the last UEFA Nations League break as Hallgrimsson picked up five points across clashes with Kosovo, Austria and two vs. Israel.
The Dubliner scored four goals in that window, but since returning to club duty he's struggled for minutes, despite Cucho Hernandez's injury setback.
Pellegrini has only started him in one in the last four LaLiga games, while in his three UEFA Champions League starts in that period, he's not completed 90 minutes once.
The Chilean was clear over what he's blaming for the situation, as Parrott aims to get back on track in Spain.
"During the international break he played four games for his national team, so we've been rotating him."
However, that angle was rejected by Hallgrimsson, who believes Parrott has the endurance to play back-to-back games with no issue.
"He should look further back, because Troy played every game for AZ. He played 90 minutes every game, fully fit.
"I don’t know if they run more in Spain. That's his strength, he’s able to play every league game 90 minutes and 120 minutes when needed, and then the games for us, that isn’t a factor.
“I don’t see him running in Spain more than he's done.
"If we need to rest him, we’ll rest him. That's always been our role. We’re not overloading players. We haven’t had many injuries in the national team."
Ireland wrap up their Nations League campaign away in Austria on November 14 and at home to Kosovo on November 17.