Sebastien Haller scored the only goal of the game after 37 minutes to secure the Hammers a vital three points - despite having a second-half Michail Antonio strike disallowed for handball by VAR - a victory which kept the Saints below their visitors.
"I don't read the media but I am not stupid," Pellegrini told BBC Sport. "If you don't get results, if you have five points from 30, you're in a difficult moment.
"I can't divide myself from the team. For West Ham it was an important three points.
"I said before the game that I felt every day the commitment of the players in the work that they do. I am happy for the players. We started the season very well and I hope now we have recovered our best performance for the next games."