Real were less than convincing on home soil, relying on the brilliance of goalkeeper Thibaut Courtois to secure a draw in the Spanish capital.
La Liga holders Barca had earlier drawn 1-1 at home to Athletic Bilbao and Madrid captain Ramos told reporters post-game: "We knew the importance of these three points to take advantage of Barcelona slipping up. The draw feels disappointing after the great job we've done.
"In the first half Atletico pushed higher, but in the second we controlled the game and just missed the finishing touch that we've had in other games. We have to look forward now.
"You always have to have the utmost respect for the opponent because in these games mistakes are decisive, so it's better to be careful and not pay the price.
"The team dug in well, controlled the game and dominated, but we've not been successful in front of goal and we've dropped points."
Dani Ceballos impressed for Real after replacing injured team-mate Gareth Bale at half-time.
Bale suffered a suspected thigh injury and Spaniard Ceballos injected some much-needed energy into Real's attack.
"I think that it was a tactical and tough contest," Ceballos said. "We did enough in the second half to have won the game. If we show the same attitude as we did tonight, we can go on and achieve big things.
"Gareth had a bit of discomfort and Julen [Lopetegui] told me to go out there and just be myself and to run at Juanfran. It's a shame that after the bad knee injury he suffered he has been unable to perform to the same level.
"We created quite a few chances. If we continue on in this vein, the goals will come. This was my best performance in a Real Madrid shirt but what I take away with me is the fact that we failed to get the win. We were the ones who put our all into winning the game. We've now got the Champions League game on Tuesday and we have to keep going."