Partridge had an impressive first season at the club after joining from Reading, and did enough to earn an extra one-year deal, with Burnett keen to see improvement.
The Daggers boss told the club’s website: “He’s done very well and played over 20 games last season, it’s good for him to get him signed up again.
“I don’t think we’ve seen the best of Matt, he didn’t have a full pre-season last year like some of the others so that should benefit him going into the new season.”
However the club missed out on signing Gavin Hoyte, who opted to join newly-promoted Barnet after he was released by Gillingham.
Burnett said: “We missed out on two players yesterday, unfortunately. We were in talks with Gavin Hoyte and we wanted to try and bring him back to the football club, but we missed out.
“We couldn’t quite match Barnet’s offer. We also missed out on a centre-forward as well which I’m disappointed about, again we couldn’t match the offer.
“Sometimes we have to wait, we signed two players who probably had the biggest contribution to our season about a week before it started last year in Jamie Cureton and Andre Boucaud.
“We are not in any rush, it’s important we get the right players in and get the very best we can.”