Chasing a fifth consecutive win over their rivals, City took a deserved seventh-minute lead through Sergio Aguero.
But by the time Aguero added his second of the match and 100th in City colours in the 89th minute, United had run roughshod over the reigning Premier League champions with a display of pace, power and tenacity that their opponents were ill-equipped to match.
First-half goals from Ashley Young and Marouane Fellaini followed by second-half efforts by Juan Mata and Chris Smalling were the sum of City's humiliation as they crashed to a sixth loss in eighth matches.
The prospect of missing out on UEFA Champions League qualification now sits alongside the ruins of City's title defence but, speaking at a post-match press conference, Pellegrini did not feel this was cause to discuss his present job prospects.
"I'm not talking about my position," he said. "It's not important."
Liverpool could move to fifth position and within four points of City with six games to play if they beat Newcastle United on Monday night.
Nevertheless, Pellegrini remains calm over his team's standing ahead of back-to-back home games against West Ham and Aston Villa.
"Winning - it's the only way," he said when asked how City could turn their alarming slump around.
"We are concerned to try and win the next game. We have to play six games more.
"We have 18 more points to play (for) so we must not make it a dramatic thing in this moment because we have to play now two games at home."
"We must try to recover as soon as we can from this defeat and try to win the next game."
