City’s hopes of retaining their European crown ended at the Bernabeu, with Dias making a costly mistake just three minutes into the second leg.
His misjudged long ball allowed Kylian Mbappe to score, setting the tone for a difficult night for Pep Guardiola’s side.
The Portuguese center-back struggled defensively, along with his teammates, as Madrid’s attack proved too strong.
Despite the disappointment, Dias refused to make excuses for the loss, acknowledging that it “hurts” but stressing the importance of learning from the setback.
He revealed that the club shares his belief in using the experience as a lesson for the future.
“Overall, we were just not good enough, the best team went through,” he said post-match.
“We are frustrated, obviously. It was a difficult moment, we were not good enough to go through it. It’s as simple as that. Ambition is always present, we always try and do our best and always try and create situations where we can actually do something.
“This year, we need to put our hands down and recognize we were just not good enough to go through.”
Looking ahead, Dias highlighted a potential advantage for City – a clearer schedule.
With no further Champions League fixtures, the squad now has free midweeks, which he believes they must use to their benefit as they continue their pursuit of domestic success.
“We win, and that’s all we do. So whenever we don’t, it hurts more,” he continued.
“It’s in times like this you grow the most. It’s something very present in my mind and in the club’s mind. There’s not much to say, hands down, shake hands, and then look forward.
“We’re still in two competitions, so we need to grow from this. It’s the only way.
“There’s no time to feel sorry. Only time to improve, keep running, and keep fighting. Tough games ahead, and we need to survive them. I don’t know if it will be a week or two weeks more playing every three days.
“Things will settle differently being out of the Champions League, we’ll have a different schedule. Look forward and grow.”