Antoine Griezmann struck twice inside the opening 22 minutes at the Riazor, before Oriol Riera pulled one back for the hosts 12 minutes from time.
Simeone, who was sent from the touchline for protesting to the officials, watched on as his side took the victory to remain third, four points clear of Valencia, who lost 2-0 at Barcelona.
"We played a great first half, where the team came out strong and won the game," Simeone said.
"Obviously, the 2-1 result is close and the other team had the enthusiasm but there was no sense of danger.
"The goals helped us manage the game better, especially in the first half. In the second half, we wanted to have more scoring chances than we had.
"[Deportivo coach Victor Sanchez] came out with a very offensive team with enormous courage to find the result.
"He played a game with players of great class, and unfortunately for them our quick goals prevented them from sticking to the plan they had."
Victory cements Atletico's position in the third and final UEFA Champions League qualification spot, but Simeone insists their work is far from done.
"It is not a definitive step because it is very tight," he said. "There are many nerves, much anxiety, much responsibility for reaching the goals that clubs want and need to be in the Champions League.
"We have a lot of responsibility and will have to sustain the effort and competition because there are many games left."
Atletico's next test comes at city rivals Real in the Champions League quarter-final second leg on Wednesday, with the tie finely balanced after a goalless draw at Vicente Calderon earlier this week.
