The Hammers went down 2-1 at the London Stadium to a Foxes side who made nine changes from the side that lost 4-0 at Liverpool on Boxing Day.
The result saw West Ham equal their club-record run of four successive home defeats in the Premier League having also lost out to Arsenal, Tottenham and Newcastle in recent weeks.
They also have nine defeats in their last 12 games, leaving them 17th in the Premier League table and hovering just a point off the relegation zone.
It was enough to prompt club bosses to part with former Premier League title winner Pellegrini after 18 months at the helm.
Mr Sullivan said: “It is with great disappointment that we’ve had to make this decision. Manuel is a gentleman and it has been a real pleasure to work with someone of his calibre.
“However, it has become clear that a change is required to get the Club back on track in line with our ambitions this season. We felt it was necessary to act now in order to give the new manager as much time as possible to try and achieve that goal.”
David Moyes is the early front-runner with the bookies to return to the Hammers.