Lionel Messi scored a brace following the red card to give the visitors a 2-0 advantage heading into the second leg next week at Camp Nou.
Albiol criticised Stark’s performance, claiming his decision had cost Madrid the game.
"The referee has decided the game. It was the only major decision [and he got it wrong]. The red was crazy," Albiol said to reporters after the match.
“We’re upset because he decided the game [when it] had been very even at 0-0 with 60 minutes played."
The defender added: “He has finished the game with that decision, the only one he had to make.
"It is key in a semi-final [and to] lose a player as important as Pepe finished the contest. It was a major decision and [because of it] we leave with a very bad result."
The Spanish international was realistic ahead of the return leg at Camp Nou on Tuesday May 3, saying it will be “difficult” to recover from 2-0 down in the Champions League semi-final.