The Welshman said he would prefer something along the lines of the old EDF Trophy, the final of which was played at Twickenham, involving just the 12 Championship clubs.
Griffiths says his views on the B&I Cup, launched back in the 2009-10 season, are shared by many of his counterparts.
Despite his criticism of the competition, not least the time and expense of trips to such as Munster A on Friday night where Knights lost 24-16, Griffiths said the club had hoped to do well at the start of their Pool 2 campaign – subsequently affected by London Welsh’s withdrawal.
He says the club treated Friday’s game seriously even though the odds of qualifying were stacked against them, and travelled over to the Irish Republic the day before.
“We gave it a good go and there was nothing between the two teams and it was disappointing to lose,” said Griffiths.
“Things could have turned out differently had (wing) Tyson Lewis, who was adamant he’d scored, not had an early try disallowed for stepping into touch.
“I was proud of the shift the boys put in and although they scored three tries we tackled our hearts out – none more so than fly-half Simon Humberstone who made 16 tackles which is a lot for a No 10.
“Latu Makaafi, who’d not started recently, made 16 hit-ups and both props played well as did the likes of Dave Nolan and Will Owen.
“We finished strongly and Sam Edgerley, who provided a bit of sparkle when replacing (scrum-half) Dan White who picked up a knock, scored a length-of-the field try.”