MILAN, Feb. 19 (Xinhua) -- Diego Costa scored a late header to give Atletico Madrid a 1-0 win at AC Milan in the first leg of their Champions League last-16 tie on Wednesday.

Milan could only have themselves to blame as they could not finish off the chances and hit the woodwork twice.

Costa then capitalised on Ignazio Abate's poor clearance attempt from a corner to nod home a priceless away goal in the 83rd minute.

AC Milan head coach Clarence Seedorf said he was proud of his side despite their loss.

"I think everyone saw what the lads did on the field. I am proud of what they did. We were a little unlucky with the goal," he said.

His Atletico Madrid counterpart Diego Simeone admitted Milan played better in the first half, but any mistake could ruin all the efforts.

"We knew that we'd be facing an intense Milan, especially in the first half. Everyone knows when you reach the knockouts any mistake can get you eliminated," he said.

The Milan side dominated the first half with excellent opportunities to open the scoring, but Andrea Poli and Kaka missed good chances, while visiting goalkeeper Thibaut Courtois was in inspired form.