"I adore Arsene Wenger, for his intellect, his language skill (knowing seven different languages is a feat!) and many more reasons", said the 29-year-old.
Speaking on RTÉ Radio's News at One, Hamilton said: "I think what has changed is what has happened on the pitch".
Attention has already turned to candidates to take over the role, with Celtic boss Brendan Rodgers, Thomas Tuchel, Carlo Ancelotti and Luis Enrique among the favourites.
And Arsenal's famous supporters have shared their reactions to his departure.
The Gunners are a distant sixth in the league, 14 points adrift of fourth-placed North London rivals Tottenham Hotspur with five games remaining. The team, however, has failed in the playoffs both years, getting the boot in the conference semifinals. The team allowed just 26 goals in those matches, with the defensive pairing of Sol Campbell and Kolo Toure dominating week in and week out. He is a proper football man, he lives and breathes it, he's dedicated to his job and his sport.
The Frenchman has lifted the FA Cup in three of the last four seasons but that has not been enough to appease some supporters.
"I hope my son can be intellectual like Arsene Wenger, and brave like (Arsenal midfielder) Jack Wilshere", he added.
For trusting me as a teenager, giving me the opportunity to express myself and grow both as a footballer and as a person. "The Premier League is about huge personalities like Arsene", said Guardiola. "The club has been relying on German know-how for several years now". Put simply, that is an entertaining style of football, opportunities for young players and a fiscal structure that safeguards the club's long-term future.
"It is power against power, it is quality against quality, it is ambition against ambition".
Gazidis reveals process to replace Wenger has started — EPL
He is a great coach. "We have to be open-mind and brave", said Gazidis, when asked about how he will select the new manager. Wenger's agent Leon Angel said on Friday that it was not the time to talk about the 68-year-old writing that elusive book.
Luis Enrique emerges as favourite for Arsenal job
Paris Saint-Germain coach Unai Emery believes that departing Arsenal boss Arsene Wenger could one day manage the French club. But there are enough reports from people in the know to suggest Stan Kroenke's loyalty to Wenger had finally run out.
Marin Cilic advances to R3 — Monte-Carlo Masters
The Spaniard is unquestionably the best mover on the clay currently playing and his court coverage will pose Thiem a real problem. The 20-year-old, who won two Masters titles last season, became frustrated in the second set but battled through 6-4, 4-6, 6-4.
Barbara Bush-Professor Investigated story — Correction
The sense of humor was on full display. "He doesn't give many answers to how he would solve problems", she told CNN at the time . Former President Jimmy Carter and his wife Rosalynn will not attend. "I saw that little body, I saw her spirit go".
Public viewing of former first lady Barbara Bush to begin
Gorbachev visited with the Bushes at the former presidents library at Texas A&M University, where Barbara Bush will be buried. Bush - her husband of 73 years - was at his wife's side when she died and had reportedly been holding her hand all day.