The Spanish director died Friday after a long battle with cancer, the magazine reported.
Despite briefly dabbling in the English-language market, Luna is perhaps best known for his so-called Iberian Trilogy, featuring 1992's "Jamon, Jamon," 1993's "Golden Balls" and 1994's "The Tit and the Moon."
The trilogy was a celebration of earthly Spanish pleasures, including the country's roadside brothels, hams and omelets, and machismo, Variety reported.
" 'Jamon, Jamon' changed my life," Cruz said Saturday in a written statement. "Bigas [Luna] was one of the wisest persons I've known, living the present and enjoying the small things in life."
"I owe Bigas the woman I love, two soulmates and a career I never dreamed I'd have," Bardem added. "When confronted with any conflict, rather than drama and anguish, he preferred a smile, love and a good slice of ham."
2014: The Year in Music [PHOTOS]