Brady and defending champions the Patriots were upstaged 20-13 by the Tennessee Titans in Saturday's AFC wild-card clash.
It was New England's first wild-card appearance in a decade as their hopes of back-to-back Super Bowl championships were dashed in Foxborough.
Attention quickly turned to Brady and his future post-game, with the 42-year-old quarterback set to become a free agent.
Asked about potential retirement, six-time Super Bowl champion Brady told reporters: "I would say it's pretty unlikely... Hopefully unlikely."
Brady's contract does not allow the Patriots to use the franchise tag on the three-time MVP, who was 20 of 37 for 209 yards and an interception against the Titans.
"I love the Patriots. They have the greatest organisation," Brady said in a news conference. "Playing for [owner] Mr. [Robert] Kraft all these years and head coach [Bill] Belichick, there's nobody who has had a better career than me, just being with them. I'm very blessed. I don't know what the future looks like, so I'm not going to predict it."
"I don't want to get too much into the future. This team has fought hard. We work hard to improve. It's proud to be part of this team every year," Brady continued."
"I don't know what's going to happen. No one needs to make choices at this point. I love playing football. I love playing for this team, I love playing for this team for two decades and winning a lot of games."
On Patriots fans, Brady – who was drafted by New England in 2000 – added: "I personally appreciate everything they've contributed over the course of not just this year but a lot of years. Grateful for the experience of playing for this organisation this year and over the course of my career too.
"I hope I've always tried to do the right thing out there. Who knows what the future holds, so we'll leave it at that."