The Reds played a full part in a rollercoaster ride of a match but despite battling back to hold a slender lead with six minutes remaining, went down 36-31 in Dunedin.
"The boys put in a big effort," former All Blacks forward Thorn told reporters.
"We had the edge there in the end, but it's about putting the foot on the throat and we missed that opportunity.
"We'll continue to work to get that ruthlessness as a team. A lot of good stuff happened for us today.
"I appreciated the composure when we were two tries down, but it's disappointing to let that opportunity slide."
The Reds finished third bottom of the Super Rugby standings with six wins from 16 matches in Thorn's first season in charge last year so taking the 2015 champions so close might have pleased some coaches.
World Cup winner Thorn, though, has always set exceedingly high standards for himself and has made it clear that his expectations from his players will be no less demanding.
The dual code international thought his pack had come under undue scrutiny from Argentine referee Federico Anselmi at scrum time - a result, he felt, of their increasing dominance.
"We've been a dominant scrum last year," he said.
"I remember at the Crusaders when we were probably the dominant scrum in the comp, the referee was often only interested in us."It was something that was frustrating and I felt that was frustrating again."
Thorn's former team are next up for the Reds when the nine-times champions make the trip to Brisbane next week and the 44-year-old knows his forwards will be fully tested at Lang Park.
"They're last year's champions and they're very experienced," Thorn said.
"They're quite a mature team. It'll be a big scrum battle with the Crusaders.
"I feel like we've been growing with our scrummaging and the Crusaders have got one of the best scrums in the comp."
(Reporting by Nick Mulvenney, editing by Sudipto Ganguly)
