The former Udinese winger has been gradually improving since his arrival at Camp Nou last summer, and his boss believes that the Catalans have made a special signing
Sanchez, a summer signing from Udinese, proved a constant menace to the home side's defence in the match at the Santiago Bernabeu, heading against the bar during the first half.
However, the Chilean winger also put in a lot of effort in defence, prompting his coach to heap him with praise.
"I want to especially thank Alexis [Sanchez]," Guardiola told reporters after the game. "He has played a fantastic game. He has stolen my heart.
"He is very young, but he came forward and sacrificed himself a lot. He is a very humble person. I think the club has made a special signing. When he is fully settled, he will do even better."
The result meant that Barca have now gone seven games unbeaten at the Santiago Bernabeu, but Guardiola did not want to dwell on that.
"I still believe that sooner or later it will end," he mused. "It is not normal, because this ground requires a lot of effort.
"The players know the importance of playing at a ground like this. We hope that the people at home have enjoyed it.
"But, looking at the game, we now have to sit back and see what we did right and wrong.
"There is still another half of the tie to come and [we] need to be at a very good level to reach the semi-finals."
Barcelona host Madrid in the return leg at Camp Nou on Wednesday, but will have to first tackle Malaga at home in La Liga on Sunday.
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