The Spanish side had to overturn a 1-0 deficit to Porto in order to reach the last eight, and Santa Cruz said that Malaga are now "living the dream".
"This is amazing," UEFA.com quotes Santa Cruz as saying. "We were dreaming about a win like this right from the time we lost in Porto.
"We thought it would be hard and it was, but now all our work has paid off. It's a fantastic achievement for Malaga and whatever happens in the next round it's already something magnificent for the club. We are living a dream.
"Now we are in the draw and of course we would like to avoid the Liga clubs because it would be nice to have as many Spanish clubs in the semi-finals as possible."
Santa Cruz, who netted the winner on Wednesday night, has scored six goals in 31 league and Champions League appearances for Malaga.