The Argentinian praised his players' reaction to the early "hit" of a Karim Benzema goal - a fightback which saw Koke and Gabi give Atletico the upper hand going into half-time at the Vicente Calderon.
But try as they might, Los Rojiblancos could not kill the game off and Cristiano Ronaldo forced the 2-2 draw with a goal eight minutes from time.
Had they held on for victory, they would have clinched their first league double over Real since 1951.
Atletico are now three points off the pace in the Primera Division title race, but Simeone believes there are enough games remaining in which they can remedy that situation.
"We started with a goal that hit us," he told his club's official website.
"We had a great reaction after the goal. The team started to play nicely: moving between lines, pressing well, playing in their rivals' area, and creating many opportunities - until the second half."
"Then their second goal came, but the team did a great job. I am proud of them.
"The result is what it is. However many opportunities you have to win the match, what counts is the final result."
Atletico have five home games remaining, and six on the road, but the last of those takes place against reigning champions Barcelona at the Nou Camp.
Speaking before Barca beat Almeria 4-1 to move second in the table, Simeone seemed optimistic his side could put themselves in a good position to compete for honours in that final-day showdown.
"Surely Barcelona will win today, but there are still 12 games before the end," he added.
"There is still time and I have no doubt that we will take three points from some of the 12 games, so that's very good for us."