Mourinho took charge of his first game as Spurs boss on Saturday lunchtime after having been brought in as the north London club’s new manager last week.
Spurs were 3-0 up early in the second half thanks to goals from Son Heung-Min, Lucas Moura and Harry Kane.
However, goals from Michail Antonio and Angelo Ogbonna made the scoreline look more appealing to West Ham United fans.
Spurs claimed all three points to notch up their first Premier League away win since 20 January.
Mourinho chose not to approach the away supporters after the final whistle, and he explained his decision after the game.
Speaking in an interview quoted by Metro, Mourinho said: “At the end of the game I didn’t want to go to our fans because I felt I shouldn’t.
“It’s about the players, not about me. Apologies for that, I stayed away.
“But I appreciate the few thousand who were there behind the team and I think really enjoying and understanding the difficulties and supporting, and probably now as happy as we are.”
Next up for Mourinho and his Tottenham team is a home clash against Olympiakos in the Champions League on Tuesday night, before a home clash against Bournemouth in the Premier League next weekend.
Mourinho was drafted in to take over from Mauricio Pochettino last week after the Argentine was sacked on Tuesday night.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news