Replays of Griffiths' 40-yard free-kick 18 minutes from time showed the ball hit the underside of the bar and bounce well behind the line, before spinning out again.
The International Football Association Board - the body that approved the use of goalline technology in the game last year - met in Edinburgh only last weekend to discuss how the various licensed systems might be implemented.
And though Fenlon kept his cool in a post-match interview with Sky Sports, he reiterated the swift need for a goalline system.
"I'm disappointed for the players to be honest," Fenlon said told Sky Sports. "I've watched the replays and it's not even close to being on the line; it's a good yard, it's almost touched the back of the net.
"Maybe the officials should be out answering questions.
"If you throw that in with the Dundee United decision a couple of weeks ago where we've had a penalty given against us, it's four big points that's cost us.
"I told (the referee) it was in. He said if he's not sure he can't give it. It's his decision but it's clearly well over the line."
Asked if the incident emphasised the need for goalline technology, he added: "I think in general that's the one area I'd like to see change.
"The fact that it's a goal and it decides the game, it's vitally important to get it up and running."
"Both halves we didn't start well but after that we played quite well," Fenlon said of his side's performance.
"I'm delighted with the players, tremendous work-rate, and it means we're unbeaten against Hearts, which is important."