The hosts were penalised for a so-called "no arms" tackle at a vital stage of the 18-13 defeat at Old Anniesland. And the incident led to official Iain Bruce chalking off a breakaway try by Robert Beattie.
Dempsey said: "I think it swung on that big decision. It was a perfectly good piece of defence and it should have been a score under the posts. But I have to admit Heriot's adapted to the testing conditions a fraction better than we did."
Heriot's chief Phil Smith added: "We have now won seven in a row, which is the best start to a campaign we have had for many years.
"It has put us in a strong position. We have always had a good, strong squad but the turnaround probably came when we fought back from 20 points down to beat Gala. That gave the boys enormous self-belief."
Keith Buchan and Max Learmonth snapped up the tries that mattered for the Edinburgh outfit, while Graham Wilson landed a conversion and two penalties.
Hawks salvaged a consolation point with touchdowns from Haddon MacPherson and Andy Linton, Scott Wight adding a last-gasp penalty.
Melrose, meanwhile, turned on the style with a thrilling second-half performance to demolish Aberdeen GR 42-16 at the Greenyards.
Damien Hoyland led the Borderers' charge with a try-double, with Joe Helps again on-form with the boot to land a series of important kicks as well as collecting a touchdown. Their other scores came from Gary Holborn, Nick Beavon, Pete Eccles and Calum Anderson.
Currie's wretched run continued when they crashed 21-12 to Hawick at Mansfield Park. But the Greens were left frustrated over their failure to cash in fully for a precious bonus point.
Lee Armstrong, Bruce McNeil and Graeme Anderson went over for the hosts, Neil Renwick kicking the rest.