In an interview with Sky Sports News, the former manager admitted that he didn't want to leave just yet, despite growing opposition from supporters' groups.
"I wanted to stay," Tuttle told SSN. "I thought I could have got the club into a better position next season.
"But I want to become a manager somewhere else, so it was decided that I should leave the club by mutual consent and try to carry on my career."
His comments will come as a surprise to many Millwall fans, who believe his negative tactics and refusal to change formations were responsible for the recent run of poor form which saw The Lions slip out of The Championship on Monday.
Tuttle recently received a vote of no confidence from members of The Lions Trust and only this week a Millwall Mad poll revealed that nearly 92% of fans would not be happy if he was still in charge next season.
"I will be putting feelers out," he continued. "And I hope another club will take a chance on me. I still have confidence in myself that I can do a good job as a manager.
"We did well at Christmas and it looked like we had turned the corner, but the 1-0 defeat at home by Sheffield Wednesday was crucial for us."