The Spaniard has faced criticism for some of his displays this season but put in a strong showing at the Bernabeu, making several crucial saves in the Red Devils' 1-1 draw.
"David's performance just showed what he is all about," Carrick told PA.
"Coming back home [to Spain] as well, there was an extra spotlight on him. Some of his saves kept us in the game at times."
The second leg of the tie takes place at Old Trafford on March 5.