The 32-year-old club captain - who has just one year left on his current contract - has had a "great run" at Watford, but he's also suggested he might not be with them again next season.
Speaking after their fate was sealed, Deeney said: "I honestly don't know if this is going to be my last game at Watford or in the Premier League.
"If I do ultimately stop playing for Watford as of now I've had a great run. Things happen in football. I have been here 10 years. If it is my time to go, it is my time to go."
Deeney joined the club from Walsall in August 2010, and has emerged as one of their modern-day legends.
In the short term, the striker is set to have a knee operation and "go and spend some time with [his] family".
Speaking to the BBC, he added: "At the end of the day they're the only people whose opinions I care about. If someone wants to give me grief online then please do it.
"I'm a big boy with big shoulders and I've had some real world issues so getting some stick online doesn't bother me."