Atletico remained top of Group E on 11 points after winning away in the competition for the first time since beating Manchester United at Old Trafford in March 2022.
Their victory also guaranteed a berth in the last 16 for Lazio, who advanced to 10 points after beating Celtic in Rome earlier in the day, and eliminated Feyenoord from the race.
“The game the team played made me very happy. An offensively correct and defensively effective match," Simeone said. "A game with very good positional play, knowing that we could create difficulty for the opponent and from that came the first goal.”
Feyenoord gave away a strange own goal as no one in their penalty box attempted to get onto a lopping ball into the danger area and it bounced in off defender Lutsharel Geertruida after 14 minutes.
In the second half Atletico went 2-0 ahead through Mario Hermoso, who hooked the ball into the opposite corner of the goal on the volley, but Feyenoord initiated a fight back through Mats Wieffer with 13 minutes left, only to see Atletico restore their two-goal advantage four minutes later through another own goal.
“I don't remember how long it's been since we qualified for the round of 16 with an advance date. That is something to highlight. The situation in our group was tight but we have managed our progress very well,” added Simeone.
Asked at the post-match press conference whether Atletico could go on and pose a real challenge for the Champions League, he said: “We are here to compete with whoever we have to compete with. With humility and wanting to improve, we know our defects and from there we try to enhance our virtues.”
They can enhance their options for the draw on December 18 by finishing top of the group and will need only a draw at home to Lazio on December 13 to ensure that.
“It is always important to finish as high as possible. We have not reached the last 16 with this kind of tranquillity for years,” Simeone said.
