Maynard, the son of former Glamorgan and England batsman Matthew Maynard, was killed after being hit by a London Underground train early on Monday morning, the day after playing for Surrey in a 40-over match against Kent.
In a statement issued through the British Transport Police (BTP), his family said: "The Maynard family would like to thank everyone for the many messages of support following Tom's tragic death in London yesterday (Monday) morning.
"As you can appreciate, the news has come as a devastating blow and although the family is grateful for all the kind messages of sympathy, we would ask that we can be left to grieve in private at this very difficult and sad time for us."
Maynard's Surrey team-mate Kevin Pietersen was among several England players who posted their condolences on Twitter on Monday.
"So unbelievably sad!! The Maynard family is so special!! Thoughts are with this special family!! Loads of love guys!! KP xxx £RIPTom".
Tom Maynard had only been with Surrey for 18 months after joining from Glamorgan when the Welsh county sacked his father as their coach.
Former England wicket-keeper batsman Alec Stewart was convinced Tom, a batsman for the England Lions, the national A team, could have gone on to the senior side, arguing decent career statistics of 2,384 runs in 48 first-class matches at 32.65 with four hundreds did not reflect the depth of his talent.
"I remember meeting Tom a few years ago during a holiday in Dubai when he and his father Matt Maynard -- a good friend of mine from our England days -- happened to be staying at the same hotel," Stewart told the BBC.
"Tom must have been about 17, but he was putting in the hard yards in the gym. Even back then, he knew where he wanted to go and that may well have been to the very top."
Stewart, who spent his entire career with Surrey, said it was hard to put into words the "sense of loss" pervading the club.
"He is the third cricketer we have lost in 15 years after Graham Kersey and Ben Hollioake were killed in car accidents in Australia, and everyone is feeling horribly numb and empty."
Mystery surrounded the closing moments of Maynard's life after Scotland Yard said he'd had run away when stopped while driving "erratically" near Wimbledon Park station, close to where he was eventually killed in an incident the BTP said Monday was being treated as "non-suspicious".
A minute's silence in memory of Maynard was held before the start of the second one-day international between England and the West Indies at The Oval, Surrey's headquarters ground in south London, with the England players wearing black armbands as a mark of respect.
On Monday, Surrey announced the postponement of their Twenty20 match against Hampshire, scheduled to be played at The Oval on Wednesday.
Glamorgan followed suit Tuesday by saying their Twenty20 match against Worcestershire in Cardiff, also due to be played Wednesday, had been postponed until July 3.