Milan had kept Diego Simeone’s side on a tight leash throughout a dramatic encounter at the San Siro but paid the price for hitting the woodwork three times in an enthralling first-half.
As the Rossoneri tired, Atletico striker Diego Costa headed an 83rd minute winner just inside Christian Abbiati near post after defender Ignazio Abate had headed a corner towards the back post.
Two weeks ahead of the second leg at the Vicente Calderon stadium, Diego Simeone’s are now favourites to qualify for what would be their first quarter-final appearance since 1997.
But Milan refuse to throw in the towel.
Former Milan great Seedorf, in his first Champions League game as coach, applauded Milan’s efforts and said the tie is not over yet.
“On the whole lads showed a lot of spirit and determination and I also saw some great individual performances,” said the Dutchman, the only player to have won Europe’s most prestigious club trophy with three different clubs — Ajax, Real Madrid and twice with Milan.
“At the end we were tired and we perhaps paid for our efforts. It’s a positive result for them but the tie is not over. I know the Vicente Calderon (stadium) well but the stadium also knows me.”
Milan spurned three chances to score in the first half, the first on 15 minutes when Adel Taarabt’s ball was put through for Kaka only for the Brazilian to send a curling left-footed strike off Thibaut Courtois’s crossbar.
Minutes later Taarabt’s cross was met by Andrea Poli but Courtois performed heroics to palm the winger’s precision header off the post.
After Emiliano Insua saw yellow for a crunching tackle on Mattia De Sciglio which left the defender hobbling off to be replaced by Abate, a Balotelli backheel on the counter found Kaka, whose latest effort skimmed the bar on its way over.
For Simeone, Atletico had a first half to forget.
“After a strong start we began suffering down the right and we weren’t sharp enough coming out,” said the former Inter, Lazio and Atletico defensive midfielder, who steered the Spaniards to Europa League victory in 2012.
Simeone boosted his midfield for the second half and immediately began to look the stronger side.
Shortly after the restart Costa was allowed space at the back post to attempt a bicycle kick when a cross was whipped but his effort was off target.
Milan created few real chances, a Kaka drive going wide and striker Mario Balotelli being restricted to free kick attempts which came to nothing.
Ghanaian Michael Essien sent a glancing header wide of Courtois’s upright but Atletico clearly had the momentum.
On 75 minutes, Costa held off his marker to set up Raul Garcia, whose drive from 20 metres was blocked down low by Abbiati.
Seedorf replaced Balotelli with Pazzini on 77 minutes but by then a tiring Milan had little left to offer.
The visitors pressed and, after a first-time Garcia effort had just missed the target, Costa struck to stun the hosts.
Milan’s last chance came from French defender Adil Rami, whose powerful freekick went a metre wide of the Atletico goal.
Kaka had plenty of reason to bemoan his earlier misses but the Brazilian was defiant.
“We created plenty of chances so I don’t want to talk about bad luck but it’s clear that if we’d had put one of those chances away we’d be talking about a different game,” said the Brazilian.
“It’s not the result we wanted but now we have to turn our focus to the second leg and believe that we can come through it.”