The Patriots signed the 27-year-old on a five-year deal in March after allowing veteran Wes Welker to leave the club during free agency.
Belichick told reporters: "Danny works hard; he's got a good skill set. He's smart, he can catch the ball, he has a good skill set and he's become a very dependable player for us, doesn't make many mental errors.
"He's a guy that's usually in the right spot, has a good understanding of defenses and what he's supposed to do. You can tell he's been in the league for four years."
The Patriots begin their pre-season campaign against the Philadelphia Eagles on Thursday.