The Argentine believes the team is evolving into the genuine article, but warned his players they must step up again when taking on Osasuna at home
Los Rojiblancos can now move joint top of La Liga alongside Real Madrid with a win in Pamplona, given Barcelona suffered a shock 3-1 loss at Real Sociedad to slip to second on Saturday.
And the coach believes his team is coping admirably with the pressure that comes with challenging for the title, while simultaneously competing in the Champions League where it beat Milan on Wednesday.
"Over the months we are getting used to the responsibility of being in this club and the need to give our best in every match," Simeone said. "For the moment we don't have to think about the Champions League until March 11. Now we have to face the match against Osasuna. We need to win it. We know we won't have it easy.
"I seek the best solutions on a game-by-game basis. Diego and David Villa did not start against Milan because I needed wide players.
"We wouldn't have needed to answer that question a year-and-a-half ago because we had no such possibilities."
Osasuna sits 14th in La Liga, just four points clear of the relegation zone, but Javi Garcia's men have not lost in their past two matches versus Elche and Getafe.
"It will be a difficult game against a rival who will feel comfortable on their own pitch, and play with an intense pace," Simeone concluded. "We have to get on to the pitch with confidence because they will be a strong opponent with great enthusiasm and creativity.
"They also need a win, like us. I think that will make a fun game."