A deflected Caolan Boyd-Munce strike and a Killian Phillips cracker put Stephen Robinson's men 2-0 up 33 minutes in.
But that lead didn’t last 90 seconds before Callum Slattery netted the first of his double.
Iacovitti said: “The feeling among the lads is that’s two points dropped - big time.
“To concede straight after we score to go 2-0 up is horrible.
“We shouldn't let that happen at all. It’s unacceptable.
“It’s a long ball, it bounces down, he hits it from 20 yards and squeezes it in the bottom corner.
“The second one is similar. They're both good finishes but it's a little deflection there which kind of kills us.
“Two goals from outside the box. We need to manage these moments - and the game - a lot better. We have to be more streetwise.”
Saints could've hurdled Motherwell into seventh by hanging on to their lead.
Now they’e four points adrift of Hearts with only three games left to haul the Jambos in.
It’s Kilmarnock up next in Paisley and the Buddies will be without suspended Toyosi Olusanya.
His second yellow for a FRUSTRATING DAY Iacovitti collision with Dan Casey was a shocking Grant Irvine call and Saints had to ride o...