Atletico's victory keeps them co-leaders with Barca with a perfect start of seven victories in seven matches, but the Argentine tried to keep pressure off his players.
"In a season, Barca and Real's financial and individual strength is bigger, we have to use our weapons and take it game by game", Simeone told a press conference. "We have to keep calm, the season is very long, we cannot be overconfident."
Atletico are level with Barcelona on top of the table with 21 points, but in second place on goal difference, and have pulled five points clear of Real.
In his nearly two years on the job, Simeone has led Atletico to win the 2012 Europa League, a European Super Cup and most symbolically, last season's King's Cup in the Bernabeu against Real.
That victory, together with Saturday's league win, suggests Atletico inferiority complex with their city rivals could have ended thanks to the combative spirit infused in his players by the 43-year-old former Argentina and Atletico midfielder.
"We are working well. The good moment we are enjoying is a reward for the team work", Simeone said.
Brazilian Diego Costa scored his eighth league goal this season, putting him level with World Player of the Year Lionel Messi, and together with Spain midfielder Koke was one of the best players in Saturday's match.
"We are a tough and competitive team, but there is something we do not negotiate on: hard work, and no individual player is more important than the team," he said, when asked about Atletico's leading duo.