(Adds details, writes through)
* Late Costa strike puts Spaniards in control
* Seedorf's first Champions League game in charge ends in defeat
By Brian Homewood
MILAN, Feb 19 (Reuters) - Atletico Madrid gave AC Milan coach Clarence Seedorf an unhappy return to a competition he graced so magnificently as a player when the Spaniards first frustrated their opponents before snatching a late 1-0 Champions League win on Wednesday.
Diego Costa scored the only goal at the San Siro with a magnificent header seven minutes from time as Atletico proved too cagey and wily for Milan, who twice hit the woodwork in the first 20 minutes of a frenetic Round of 16 first-leg game.
Atletico, with coach Diego Simeone prowling the touchline in his familiar all-black outfit, tweaked Milan's nerves with repeated tactical fouling in midfield, giving away 20 free kicks
"We are a normal team and we try to profit from the situations we create," former Argentina captain Simeone told reporters. "We work with humility, we started gaining metres and we felt better as the game went on."
Milan, the only Italian survivors in the competition, had the better of the first half and players such as Kaka and Adel Taarabat showed odd flashes of skill to bring the San Siro to life.
However, awful defending after halftime gave Atletico encouragement and the Spanish side closed in for the kill in the last 20 minutes.
Dutchman Seedorf, who won a record four Champions League titles as a player with three different clubs, took over for his first coaching job in January after Massimiliano Allegri was sacked and is still settling into his new role.
"In the last 20 minutes, we paid for the effort we put in and we were less lucid, these things happen," Seedorf admitted.
Both sides showed their limitations in a first half which was fast and furious but also scrappy and littered with mistakes.
Milan were unlucky not to take the lead when Taarabt slipped the ball to Kaka on the edge of the area and the Brazilian produced a delightful first-time shot with his left foot which goalkeeper Thibaut Courtois managed to tip on to the crossbar.
Milan were foiled again three minutes later when Taarabt curled a cross over from the right and Andrea Poli's downward header was tipped on to the foot of the post by the Belgian goalkeeper.
Former World Player of the Year Kaka was again a threat when he curled another shot just over the top with his right foot, this time from Mario Balotelli's clever backheel.
Balotelli also had a chance after a dreadful Gabi clearance but he side-footed his shot wide from the edge of the penalty area.
However, the hosts lost momentum after halftime and began to look shaky at the back.
At one point, Milan twice lost possession in their own third of the field in quick succession as they tried to play their way out of defence.
Kaka had another good opening just before the hour when he collected Ignazio Abate's pass, slipped past two defenders and shot just wide of the far post.
But, while Balotelli wasted several free kicks for Milan, Atletico were gaining in confidence and began threatening in the final 20 minutes and it was no surprise when they went ahead.
The visitors won a corner on the right, the ball deflected off the head of Abate and Diego Costa at the far post produced an astonishingly athletic leap to head his fifth goal of the competition. (Editing by John O'Brien)