The Uruguay striker fluffed an attempted header in the ninth minute at the Calderon stadium but his follow-up effort evaded goalkeeper Pepe Reina and defender Jamie Carragher and squeezed just inside the post.
Liverpool's journey to the Spanish capital via Paris had taken 24 hours due to airspace restrictions and the Premier League side, missing former Atletico striker Fernando Torres, struggled to build any momentum after falling behind.
Liverpool coach Rafael Benitez fielded a cautious-looking starting team, with defensive midfielders Lucas and Javier Mascherano both included and David N'Gog alone up front.
Reina twice saved them from falling further behind in the second half. The Spaniard pulled off a fine reflex stop to deny Simao Sabrosa and later flung himself to his right to block a powerful Tomas Ujfalusi strike as dominant Atletico pressed for a second goal.
"We are happy but we know that we have to play another 90 minutes and it's going to be difficult," Forlan said.
"It's going to be hard. They play well at Anfield and they are a very strong side," added Forlan, who scored two goals for his former club Manchester United to win a Premier League match at Liverpool's home ground in 2002.
After a minute's silence for former International Olympic Committee (IOC) president Juan Antonio Samaranch, who died on Wednesday, Atletico seized control.
Liverpool's only real chance of the first half came in the 19th minute when captain Steven Gerrard raced clear but his left-foot strike under pressure flew well wide.
Atletico, who have struggled in La Liga but are also through to the King's Cup final, passed the ball confidently and the often erratic Luis Perea was a rock in central defence.
The return leg is next Thursday and the winners play Hamburg SV or Fulham, who drew 0-0 in Hamburg on Thursday, in the final in the German port city on May 12.
Meanwhile, Fulham shrugged off the effects of 17 hours travelling on a coach to hold Hamburg SV to a 0-0 draw in the first leg of their Europa League semifinal.
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