Pochettino was sacked and replaced by Jose Mourinho on Wednesday, despite leading Spurs to a UEFA Champions League final last season.
The Premier League club pulled the pin on Pochettino's five-and-a-half-year tenure with the club languishing 14th in the competition.
Pochettino's assistant Jesus Perez used Twitter to share the Argentinean's heartfelt goodbye on a tactics board, having been unable to say goodbye personally.
"Big thanks to you all," Pochettino wrote in a picture posted on Friday (AEDT).
"We can't say goodbye… you will always be in our hearts."
Pochettino's future has dominated headlines since his Tottenham departure.
The 47-year-old has been linked to Bundesliga champion Bayern Munich as well as Tottenham's Premier League rival Manchester United, which reportedly was keen on Pochettino before turning to current boss Ole Gunnar Solskjaer.
Real Madrid and Paris Saint-Germain have also been touted as potential destinations for the Argentinian.