The Stamford Bridge crowd gave Mourinho a standing ovation and sang songs in support of the under-fire manager.
Speaking after the match, which his side won 2-1, Mourinho said: "The moment I came back to the club and we played the first match at home against Hull City, the way the club and stadium welcomed me was amazing."
"But not comparable with today because today comes in a moment where the results are not good. It comes in a moment where you [the media] are asking for my end.
"The fans read newspapers, the fans watch TV, the fans listen to pundits and commentators' opinions, they read blogs."
"It is quite unbelievable what they tried to say today. Today they tried to say 'we want you here' and probably they want also to say to all of you 'let him work, we want him, let him work. It is a fantastic feeling."