The 31-year-old???s release by the Tyneside club was confirmed on Friday afternoon and he took to Twitter to share his thoughts on Ashley as he prepares to move on after a seven-season stay.
Posting on his account @elgalgojonas, Gutierrez said: ???Two things I learn from my illness, how you can support a player (Newcastle fans) and how you leave a player alone (Newcastle owner).???
He added on Facebook: ???Thanks to all football fans and Newcastle fans for supporting me and trust in me.
???This is a way to demonstrate I always hear you. You are very important to me, football wouldn’t be the same without you. All my effort and affection is for you!???
Gutierrez has since made a full recovery and after returning to action in March, he set up one goal and scored the other on the final day of the season to ensure Newcastle avoided relegation from the Premier League with a 2-0 win against West Ham.
His exit from St James??? Park had, however, been widely expected after he was told towards the end of last year he should find a new club.
Before Gutierrez’s departure was formally announced, he urged Ashley to consider what must be done to move the club forward after a last major trophy win in 1969.
Asked what needs to happen at Newcastle this summer, he told the Shields Gazette: ???That???s a good question for the owner.
???I think the club has to learn what has happened in the last few years when they have been in charge of the club.
???It???s important to think about good and bad decisions. It???s good for learning, and to improve. They have to take note about what has happened during the last few years.
???They have to think what they are going to do, if they are going to go forward. They have to think about what is best for the city.???