It is believed the 30-year-old had been in line to replace Mark Noble in the 70th minute, but Colombian midfielder Carlos Sanchez came on in his place.
While Perez was also a candidate to replace the injured Marko Arnautovic in the 64th minute, but Michail Antonio was preferred instead.
Sky Sports had reported that the ex-Arsenal ace – who could be seen arguing with West Ham's goalkeeping coach Xavi Valero on the dugout – refused to get himself ready on the touchline.
Speaking after the game, Pellegrini said: "Maybe it looks bad? But Marko [Arnautovic] was injured and I called Luca to start his warm-up.
"But when I saw Antonio was ready I decided to bring him on instead."
Former Liverpool and Manchester United striker Michael Owen said of the incident: "No matter what you get paid to play. And you get asked to do something you got to do it.
"We’ll find out, hopefully, what the reason is, so I’d only be speculating. But that’s the line to cross that you shouldn’t cross."
Sports reporter Ian Abrahams tweeted: "Lucas Perez refusing to warm up? Bloke’s lucky he’s on the bench. Shown very little either at Arsenal or West Ham, that he is good enough."
While Millwall's Head of Coaching Kenny Brown said: "Lucas Perez refuses to warm up with 20 mins to go. Incredible lack of respect & professionalism."
Perez is yet to start in the Premier League for West Ham following his move from the Gunners.
While he failed to impress against AFC Wimbledon in the EFL Cup as the Hammers edged out a 3-1 victory.
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