Forfar looked to be returning to Angus with a point for their efforts at Borough Briggs on January 2 only for Darryl McHardy to net for the hosts three minutes into stoppage time.
Despite the defeat, Forfar remain second in League Two and Irvine wants his side to pick up their momentum again this weekend when they host Stranraer.
"It’s a real downer for everybody,” the boss told the club’s social media channel.
"But we need to learn from that, pick ourselves up and work hard in training.
"We’re at home next weekend and we need to get back to winning ways.”
Reflecting on the Elgin defeat, the manager believes Elgin set out to stifle his side and he admits it worked in the end.
“Elgin obviously had a game-plan that involved frustrating us and relying on set-plays,” Irvine added.
“We played into their hands at the end by giving away a silly free-kick which led to the corner and the goal.
"Set-plays are so important in football.
"I’ve been preaching that since early in the season when we were falling victim to a number of late goals from set-plays.
"I want to go into training on Tuesday and work hard on correcting what I saw.
"We don’t want to go down that slippery slope again and concede any more goals from set-plays.
“The biggest regret is that we knew McHardy was a real threat at corners and free-kicks. He has scored a few goals for them this season.”