The Argentinian was sacked last week after five years in the job following Spurs’ slump in form, before being swiftly replaced by Jose Mourinho.
Pochettino took the north London club to the Champions League final last season, where they were beaten by Liverpool in Madrid.
In a statement issued through the League Managers Association on Thursday evening, Pochettino said: “I would like to thank Joe Lewis and Daniel Levy for giving me the opportunity to be part of Tottenham Hotspur’s history.
“I would like to thank also everyone I met at Tottenham, all the club staff and the football players during these five and a half years.
“Finally I would like to give a special mention to the fans who make this club so great with their fantastic support.
“I gave the best of me to accomplish the objectives I was asked for in our first meeting. There were equally tough challenges as exciting success.
“Best wishes for the future, I am sure we will cross paths again.”
Former Espanyol and Southampton boss Pochettino has been linked with a swift return to the game, with Manchester United and Bayern Munich suggested as potential destinations.