The Argentine coach praised the performance of his team after they extended their 100% record into a fifth game
Second-half goals from Raul Garcia and Diego Costa saw los Colchoneros take all three points back to Madrid, leaving them second to Barcelona at the top of the table only on goal difference.
Speaking after the game, Simeone was delighted with his side's display and the grit they displayed to ensure they ground out a victory against resilient opposition.
"We waited for our moment and we took advantage of our virtues," the 43-year-old Argentine told Marca.
"We played with a strength and persistence that has made this team so successful."
Atleti have been in excellent form so far this season, scoring 16 times in the league this season and making a successful start to their Champions League campaign by defeating Zenit St Petersburg 3-1, but Simeone was keen to stress that the victory over Pucela was far from routine.
"In the beginning there was some uncertainty with Valladolid, mainly because we did not know which team would line up. They had a great first half and did not let us feel more comfortable," he continued.
"In the second half the team did a great job and we could take advantage of our chances."