Each card was personally signed by Allardyce and sent out to every member of the squad that beat Slovakia, with the aim of promoting a feel of togetherness ahead of next month's World Cup qualifiers against Malta and Slovenia.
The message on the postcard, which was sent out by the Football Association (FA) the same day as Allardyce's 67-day tenure ended, read: "Well done! Our journey has begun with our first win together. Looking forward to seeing you soon."
Gareth Southgate, coach of the under-21 side, will take charge of the senior team on a caretaker basis for the next four matches, including three World Cup qualifiers and a friendly against Spain.
(Reporting by Ian Rodricks in Bengaluru; Editing by John O'Brien)