Saul Niguez's 21st-minute strike looked set to secure a valuable home win for Diego Simeone's men, but Luis Suarez hit back eight minutes from time to earn a result Barca's second-half performance deserved.
While the visitors had further chances to take all three points, Valverde was content with a draw that keeps his side unbeaten in La Liga after eight matches this season.
"I have a positive feeling from the game," he said. "We must value a point against a great rival who had taken the lead — Atletico normally manage their lead very well.
"In the first half, we found it difficult to make chances. After half-time, we were able to break up the game. We were more exposed, but we had more chances.
"[After the equaliser] we had chances to win the match, too. It was a great game in general, with a great atmosphere."
On goalscorer Suarez, who netted for just the third time this season, he added: "Suarez did very well, even apart from goal.
"The confidence of forwards can change very quickly — especially when they score. He worked very well in the area and hopefully he can go on a good run."
Suarez felt his side deserved more than a point, however, based on their performance after the break.
"In the second half, we had many chances and deserved more than the draw," he said. "I'm happy to score the goal, but it's more important to help the team so they do not lose. I always try to help."