Postecoglou was axed by Levy despite winning the Europa League title - a first UEFA trophy for the club in 45 years. The triumph also qualified Spurs for next season's Champions League.
But their 17th place finish in the Premier League has seen Levy sack the Australian, despite the support he enjoyed from the dressing room.
After the news broke, fullback Pedro Porro posted to social media: "Thank you for everything, boss. For mentoring me early on, helping me settle into the club, and trusting me out on the pitch.
"I’ll always be grateful for the way you led us, defended us, and kept us going through all the highs and lows. Above everything, you gave us one of the greatest moments in the club’s history and for that, you’ll always be celebrated. Wishing you all the very best, boss."
Richarlison said: "Mister, massive thanks for helping me out and believing in me during one of the trickiest periods of my carreer and my life.
“Everyone who loves the Spurs will remember that Big Ange always bags trophies in his second season. We've made history! Cheers and good luck on your journey! I'll always be rooting for you."
Thank-you gaffer
Fellow forward Dominic Solanke added: "Thank you for bringing me to this wonderful club, thank you for bringing us a wonderful trophy, Won't ever forget the convo we had before I signed and we achieved a dream! All the best in your next adventure."
Lucas Bergvall said: “Thank you for everything you have done for me. Thank you for bringing this club a European trophy and memories to last a lifetime for us and every Spurs fan around the world. Wishing you all the best."
Micky van de Van also stated: “Gaffer, Thankyou for everything! Believed in me from the first day I arrived at the club.
“Many ups and downs in the last two years but you kept believing in us and kept pushing us.
“Big part of the success from the club this year, and forever grateful that u made me part of it. All the best.”