England fell to their first ever home series defeat to Sri Lanka on Tuesday after Cook had allowed a strong first-innings position to slip on day four at Headingley.
Australian leg-spinning great Warne, who has been accused by Cook of having a personal agenda behind the attacks on his leadership, has ridiculed the 29-year-old's performance during the loss in Yorkshire, claimed that he has no tactical nous and urged him to step down as Test captain.
"On Monday at Headingley I witnessed the worst day of captaincy I have ever seen at international level in almost 25 years in the game," Warne told reporters.
"There are three ways to go with Alastair 'Cooked' Cook. Everyone sticks their head in the sand and just allows things to keep going as it is and hope he finds form with the bat and by a miracle discovers some tactical brains from somewhere.
"Two: he steps down from the captaincy to concentrate on his batting. Three: the most radical of all, he has a complete break away from the game. Lots of people, including me, think it is time for him to step down as captain."
Cook, who oversaw the 5-0 Ashes drubbing this winter, was appointed as Test captain in August 2012.