The fullback announced his decision last week and he was booed mercilessly by home fans during Sunday's 2-2 draw with Arsenal.
Walker, now on-loan with AC Milan, said on his personal podcast: "He would have had very long, sleepless nights on what he had to do for his career.
"The servant he has been for the club, for the trophies he has won, the player he has become, me personally, you have to say thank you and wish him all the best on his next chapter.
"When Real Madrid come knocking at the door, there are not many people who would turn that down. For Trent, it would have been a very tough decision because I know the love that he has for not just the club but the city.
"Maybe he feels he has achieved what he wants to achieve at his boyhood club, he has won every trophy you can do and he wants a new test and chapter.
"You have to wish him all the best and hopefully he goes and produces what he has produced at Real Madrid."