Remy scored two minutes after replacing the injured Diego Costa at the KC Stadium, and Chelsea will be concerned about the Spain international’s previous hamstring problems going into the business end of the season.
But Mourinho insists his side have options if Costa is injured for the Premier League return in a fortnight against Stoke, one of those being Remy.
He told Sky Sports: “Every time he plays, scoring or not scoring, he gives us everything he has to give.
“Sometimes it is movement, sometimes it is defensive contributions, sometimes he is scoring goals.
“This is a goal that means two extra points and I’m pleased for the boy, he is a fantastic kid.”
Mourinho insists he was calm with his players at half-time after Hull came back from two goals down to score twice in the space of two minutes.
Thibaut Courtois’ mistake led to Abel Hernandez’s equaliser after it had looked like Chelsea would cruise through the clash, but Mourinho refused to focus on individual mistakes.
“There are team talks and there are team talks, our one was a calm one.
“Not to reflect on the mistakes we made defensively, I had complete trust our players would be back to a good performance defensively.
“We had to start the second half exactly in the same direction.
“The victory is very, very imporant obviously, to go back to three points after a draw in the last game at home.
“The performance in my opinion was very, very good. We played fantastic football until the 2-0, obviously we lost a little bit of quality after their two goals.”