Despite Brady's exit, the Patriots ended the 2020 NFL Draft without using any of their 10 selections on a QB – passing on 23rd pick Jordan Love.
It left Jarrett Stidham – Brady's backup last season – and veteran Brian Hoyer as the only quarterbacks on the roster in New England, where the Patriots reportedly agreed to terms with Louisiana Tech's J'Mar Smith as an undrafted free agent.
"If we feel like we find the right situation, we'll certainly draft them. We've drafted them in multiple years, multiple points in the draft," Belichick said following the conclusion of the third and final round of the draft on Saturday.
"Didn't work out the last three days. That wasn't by design. We just tried to do the best we could with what we had this weekend."
Stidham was drafted by the Patriots in the fourth round of the 2019 NFL Draft. He made three appearances last season, throwing for 14 yards and an interception.
Journeyman quarterback Hoyer is in his third spell with the Patriots following stints in 2009-2011 and 2017-18.
Belichick added: "I like both those players. We've had Brian a couple times. I think he certainly gives us a very solid level of play. We have a lot of confidence in him.
"And Jarrett had a good year last year. He improved a lot. We'll see where that takes him. Yeah, I have confidence in both players."