After a shaky start on Wednesday, Milan grew in confidence and began to dominate the San Siro clash, and they should have been ahead at the break after creating a number of excellent first-half chances.
However, those opportunities were wasted and after a handful more in the second half, the Italians were punished by a late Diego Costa header that gives Atletico a slender advantage to take into the second leg.
Despite the defeat, Seedorf was happy with his side's display and felt that there were plenty of positives to take out of the game.
"I think everyone saw what the lads did on the field. I am proud of what they did," he told Sky Sport Italia.
"In the last 20 minutes we lost our intensity and Atletico started to get closer, even without creating that many chances.
"We were a little unlucky with the goal, but I saw some very good responses in the first half.
"The Vicente Calderon is a fiery atmosphere, but that stadium knows me too. I had some good times there (as a Real Madrid player)!
"I say the players and fans have every right to be optimistic and to believe."
