Barry's reckless lunge resulted in a red card from referee Martin Fox - and left Tait requiring extensive treatment, including use of an oxygen mask, before climbing gingerly to his feet.
Barry will now face a Rugby Football Union disciplinary hearing and possible ban, just as third-placed Quins begin preparations for the closing stages of their league campaign.
But rugby director Richards said: "De Wet has apologised to Mathew and he has apologised to me.
"He has an unfair reputation as a dirty player and he doesn't deserve it."
Despite the loss of Barry, Quins defeated struggling Newcastle 15-9 at the Twickenham Stoop thanks to four Adrian Jarvis penalties and a Danny Care drop-goal.
They were the only side among the top four to win this weekend as a sixth victory in seven games left them just two points behind leaders Gloucester.
And another assured display by the uncapped Care unquestionably enhanced his prospects of making England's tour to New Zealand in June.
Richards added: "If three scrum-halves go on tour to New Zealand this summer, then Danny Care should be one of them.
"What the management have to consider is when is the best time in a player's development to cap them in New Zealand - it's a heck of a place to win your first cap."