The Highlanders needed to win and hope for a favour from Dumbarton against Dunfermline but the dream did not materialise as the Pars took care of their own business.
Inverness will be left ruing a poor start to the season as their impressive late run of form, going unbeaten during nine games in April, did not show any sign of ending against a poor Morton side.
However, manager John Robertson pointed to last Saturday’s draw with Dunfermline as the decisive moment in the season.
“All we could do was keep Dunfermline honest – we’ve gone unbeaten in 13 with 32 points from 36. I’m really proud of the boys’ efforts but congratulations to Dunfermline because we have thrown everything we had at them.
“It’s all boiled down to the 95th-minute goal we conceded. It was still in our hands with three games to go but a brilliant header from Nicky Clark has cost us, that’s the definitive moment. That’s what it boils down, you can forget losing 5-1 earlier in the season or the poor start in general.
“We need to start next season how we finished this.”
The newly formed strike partnership between George Oakley and Nathan Austin has been instrumental in Caley’s late surge and both were on the scoresheet once again.
Oakley, pictured, made the breakthrough when he out-muscled a defender to bundle home an in-swinging Liam Polworth cross after 20 minutes. Ian Vigurs, brilliant throughout, smashed two free-kicks off the bar as Caley dominated proceedings and they deservedly doubled their advantage on 37 minutes.
Charlie Trafford threaded a brilliant pass through to Oakley and he smashed an effort from the angle underneath Connor Brennan to notch his 12th goal of the season.
Cappielow midfielder Gary Harkins was fortunate not to be shown a straight red for pulling back Vigurs after the Inverness captain dispossessed him and raced towards goal.
Morton improved after the interval, Mark Ridgers brilliantly tipping a Harkins free-kick on to the bar and Robert Thomson came agonisingly close to pulling a goal back when his low angled shot hit the post.
But Austin finished the game as a contest ten minutes after the break when he tapped into an empty net after his initial shot was saved by Brennan but rebounded to the striker.
Morton boss Jim Duffy said: “It’s very disappointing. The last six-seven weeks we haven’t been good enough.”