Mourinho's men were held to a 1-1 draw by the Reds on Sunday, with Gerrard cancelling out John Terry's opener at Stamford Bridge.
The result ended the Merseysiders' hopes of a fourth-placed finish and earning a return to Champions League football next term.
"I will miss him, yes," Mourinho, who tried to sign Gerrard for Chelsea, Inter and Real Madrid, told Sky Sports. "I want my league to be always the best league. I want my league to have always the best players.
"I saw the end of amazing players and I was always hurt by that. Luis Figo played his last game with me with Inter, Steven is leaving, Frank Lampard is leaving ... [Jamie] Carragher also a fantastic enemy, he left last season.
"This is Mother Nature: You can't stop it but you can get great memories of great opponents."
Gerrard received a standing ovation from both sets of fans when being substituted but disregarded the Blues supporters after the game. Mourinho, though, insists it was a touching moment.
"I think Stamford Bridge was fantastic because the negative song is the song that shows exactly [what] that 'dear enemy' concept means.
"In the end, to get an ovation at Stamford Bridge I think is special for him and I think it shows exactly what I'm saying. We have a lot of respect for the top guys."