Milan head coach Seedorf witnessed his side fall to a 4-1 defeat at Vicente Calderon's in Tuesday's last 16 second leg tie, as Atleti completed a 5-1 aggregate victory.
Kaka - who used to play for Atleti's rivals Real Madrid - sparked hopes of a comeback by cancelling out Diego Costa's early opener.
However, a fortunate Arda Turan volley put the hosts ahead before half-time, while a Raul Garcia header and Costa's second in the closing stages meant there was no way back for the Serie A outfit.
Seedorf believes the turning point came when Turan restored Atletico's lead and he lamented a lack of consistency from his charges.
"You could see after the second goal that the team struggled psychologically to react, as they often do," he told Sky Sport Italia.
"The second goal turned off the light and sapped the energy from the team.
"We analysed the situation together. Obviously the Champions League was an important objective for us and economically for the club.
"We had played well in the first leg and showed in the first half (on Tuesday) we could play on a par with Atletico, but couldn't be consistent for the whole game."
With the side currently 10th in Serie A, Milan's chances of playing European football next season are fast diminishing.
Yet, Seedorf insists he has no regrets about replacing Massimiliano Allegri as coach in January.
He added: "I am absolutely convinced I made the right choice. I wore these colours for 10 years, the president gave me so much and the club is trying to rebuild what has been lost.
"This request pleased me and it was not ideal to take over midway through, but we are preparing for the future and trying to end the season as best we can."
