Lukaku joined Roma on a season-long loan from Chelsea and has reunited with Mourinho, who worked with the 30-year-old at the west London side and Manchester United. Lukaku spent last season on loan with another Serie A club, Inter Milan.
Roma's 7-0 home trashing of bottom-placed Empoli earned them their first win of the season, with Lukaku netting their sixth in the 82nd minute.
When asked what frame of mind Lukaku was in when he moved to Roma, Mourinho said: "Happy".
"Romelu needs to feel loved and wanted," he added. "When he came here, he could sense the team needed a player like him. I think he's really happy.
"He likes to win - that's in his nature."
Mourinho also said getting off the mark at Roma would have been good for the Belgian's confidence.
"That wasn’t a big deal for me. Maybe it was for him – you know what footballers are like, especially forwards, they live to score," he added.
"He’s an intelligent player who since arriving has made it clear that first and foremost what matters is that Roma score, not that he scores."
Roma moved up to 12th with the win and on four points from four matches. They next face Moldavan club Sheriff Tiraspol in the Europa League on Thursday before visiting Torino in the league on Sunday.
