FOXBOROUGH, Mass. -- New England Patriots quarterback Tom Brady had said in the immediate aftermath of Saturday's playoff loss to the Tennessee Titans that it was "probably unlikely" and "hopefully unlikely" that he would retire, and now he has expanded on the topic, writing on social media that he has more to prove.

In an Instagram post Wednesday morning, Brady wrote, "In both life and football, failure is inevitable. You don't always win. You can, however, learn from that failure, pick yourself up with great enthusiasm, and place yourself in the arena again. And that's right where you will find me. Because I know I still have more to prove."

Brady wrote that his Instagram post came after "a few days of reflection," and he wanted to say thank you to fans.

Brady, who turns 43 on Aug. 3, is scheduled to become an unrestricted free agent on March 18. The Patriots can't assign him the franchise tag, which gives Brady leverage to dictate his plans.

Patriots owner Robert Kraft told Peter King of NBC Sports that his "hope and prayer" is that Brady either plays for New England or retires.

Meanwhile, Patriots coach Bill Belichick said Sunday that more time was needed to decide how the team views Brady's future, as well as other free agents. Belichick acknowledged that Brady is an "iconic figure in this organization."

In his Instagram post, Brady wrote to fans: "I am so grateful and humbled by the unconditional support you have shown me the past two decades. Running out of that tunnel every week is a feeling that is hard to explain. I wish every season ended in a win, but that's not the nature of sports (or life). Nobody plays to lose. But the reward for working hard is just that, the work!!

"I have been blessed to find a career I love, teammates who go to battle with me, an organization that believes in me, and fans who have been behind us every step of the way."

Brady referenced a quote from Theodore Roosevelt, president of the United States from 1901-1909, saying the Patriots gave their all for a worthy cause while preparing "to fail while daring greatly."

"And for that, we've been rewarded with something that the scoreboard won't show -- the satisfaction of knowing we gave everything to each other in pursuit of a common goal. That is what TEAM is all about," Brady wrote.