Gutierrez recently revealed he is undergoing treatment for testicular cancer in his native Argentina.
The 31-year-old midfielder - out of contract at the end of the Premier League season - was told to find a new club during the close-season.
In an interview with British newspaper The Chronicle, Gutierrez said: "I don't want to say if they were good or bad, I can't judge.
"What I can say is that it hurt me very much when they told me to look for another team after that I had the surgery.
"I had been at the club for five years – that was tough."
Gutierrez, however, was very thankful to Newcastle fans for their ongoing support.
"I am very happy for what the Newcastle fans did, and thankful to the supporters of Velez Sarsfield and Almagro," he said.
"I am also thankful to all the people linked to football because I have received very nice messages from them.
"All this gives me more strength not to give up."
