Substitute Michael Higdon came off the bench to turn home Jackie McNamara's inviting cross after 68 minutes to rescue the Bairns from the drop.
Falkirk capitalised on their numerical advantage after Ross Tokely had been sent off for a last man foul in the first half.
Inverness boss Terry Butcher believes Tokely's sending off was a massive factor behind the defeat.
He said: "I have only seen the incident once but I think there was doubt about it being a goalscoring opportunity. But there is no point being bitter. We have had opportunities to get ourselves out of trouble and we only have ourselves to blame."
The Inverness boss said he was very proud of his players, despite finishing bottom of the league on goal difference.
He said: "My players have been fantastic for me and they have given everything for the club. To lose out on goal difference is a really bitter pill to swallow.
"I thought we did really well today and everything looked to be coming to fruition before the red card came along. But the players were tremendous after that and we had chances at the end to get back level.
"We weren't far away and that makes it even more galling and soul destroying. Had we been relegated seven or eight games ago it may have felt different but to have gone so close is very hard to take."
Butcher added that his heart went out to Tokely for his part in the club's defeat.
He said: "Ross is devastated but he shouldn't feel bad as he has been one of the key members of our squad and he has been terrific for us."