The Dutch champions threatened Los Rojiblancos in both halves, just as Diego Simeone expected, but Los Rojiblancos were able to defend well while also benefitting from a few odd refereeing calls.
"It was a tough game, but we knew it would be," he told beIN Sports after the final whistle.
"PSV is a team that works very hard and which had a similar plan to that of [last season's last 16 second leg at] the Vicente Calderon, which was to hit us on the counter attack with [Luciano] Narsingh.
"We tried to hurt them a bit more on the left side."
Simeone admitted that there was a change of approach for the second-half.
"The goal arrived and then in the second-half we tried but were unable to solve the match with the counter attack," he said.
"Yet the players' effort was tremendous. We have secured an important victory."