Real have now scored 16 goals in three La Liga outings, climbing above Barcelona to the top of the table and looking increasingly capable of ending their arch rivals's two-year grip on the title.
Mourinho's in-form Portuguese compatriot Cristiano Ronaldo hit four goals against Racing at the Bernabeu, taking his tally to eight in three league games and nine for the season.
"We have been playing very well for several games now, working and pressing like a team," Mourinho told a news conference.
"People can find themselves in a state of euphoria but we need to be very calm. Great coaches and great players cannot allow themselves to be euphoric with little to show for it."
Unbeaten Real have 20 points from eight matches, one ahead of Barcelona who won 2-0 at Real Zaragoza earlier on Saturday thanks to a double from Lionel Messi, his second in a row after Wednesday's two Champions League goals against FC Copenhagen.
The flamboyant Mourinho has repeatedly stressed his new team are under construction following his close-season move to the Spanish capital from Inter Milan.
He acknowledged on Saturday that Real's demanding fans were enjoying their recent devastating run but sounded another note of caution.
"We are growing little by little," he said. "The team is in a very positive moment and we have to carry on without much time to rest or enjoy it.
"Of course I like it (when we win) but we shouldn't think this is going to happen in every match.
"There will be narrow victories, draws and defeats. We want more important results than this," added Mourinho.
