The hosts blew a 20-3 lead as Delon Armitage’s try on the stroke of half- time sparked a stunning turnaround at the Stoop.
It was the second week running that Richards had seen his side collapse after dominating the early exchanges.
Tom Guest and Ugo Monye finished off superb team tries, while winger David Strettle was back to his best.
But they ran out of steam in the second half.
Richards, however, has no intention of switching to the sort of negative rugby being dished up by Quins’ Premiership rivals.
He said: “We want to play and we will carry on playing. Why should this result cramp our style?
“The crowd will have gone home saying ‘What a fantastic game’. We were just disappointed to lose.”
Danny Care’s 78th-minute try handed Quins a bonus point but came too late, while Irish’s Peter Hewat fired 18 points.