Wainwright and lock Ben Carter were the only players from the Rodney Parade club to get the call from Tandy for the Six Nations despite strong recent results.
Dragons provided five players for the autumn internationals but hooker Brodie Coghlan and injured tight-head prop Chris Coleman miss out along with Dyer.
Tiatia revealed that the Wales coaching staff contacted Coghlan, scrum-half Che Hope, blind-side flanker or lock Ryan Woodman and full-back Angus O’Brien after they missed out on the squad.
“What’s been really good is that they’ve communicated around areas that players need to get better at and keep improving,” said the Dragons boss.
“I’m disappointed that we didn’t get many in the squad but what I can control is working with our players and being really clear on how they shift forward.
“They’ve just got to be razor-sharp ready if called upon.”
Dragons travel to Munster and Ospreys before a break for the start of the Six Nations.
They host Benetton on 28 February and hope to have Wales hooker Elliot Dee, who has not played since the opening weekend of the season, in contention for that game along with tight-head Dillon Lewis.
