Simeone not drawn into Atletico title talk
An 11th-minute goal from Diego Costa was all the visitors needed at the Santiago Bernabeu as they made it seven wins from as many La Liga matches this campaign.
While it meant Atletico kept pace with league leaders Barcelona and moved five points clear of Real, Simeone said it would be tough for his side to challenge for the championship.
"It would be perfect to say now we can bet for the title," Simeone said.
"But I think the same I told two days ago, in such a big season, the economic power (of) Barcelona and Real Madrid are bigger than us.
"We will try with our weapons, playing match by match and we will try to give everything in every match."
Simeone warned his team against looking too far ahead despite their bright start and said they needed to stay focused.
"Be patient because La Liga is really long. You are used to watching a lot of things in football," he said.
"You cannot look at what you have done. In football it is about day by day."
The victory was Atletico's second straight win over Real after they broke a 14-year wait to beat their city rivals again with their Copa del Rey success in May.
Simeone praised his players but said winning a trophy at Real earlier this year was a bigger achievement.
"A final is always better than any other thing as you have said and obviously I put a value on winning a final at a rival's stadium as we won last year because we did from a 1-0 down to get back in 2-1 up," he said.
"Tonight the players did an awesome match as usual from the tactic and psychological points of view."
Simeone said his tactics worked well against Real as Atletico looked to exploit the spaces between the lines.
"We already knew we could find room between their lines. We understood it and after that we had to take advantage on Diego Costa's speed," Simeone said.
"He did an awesome job and we could do more times because we missed two chances on two counter-attacks and one to one situations, which is difficult to get."