Cristian Chivu's free-kick put Inter on track for a second Serie A win in three games but the visitors promptly replied through Riccardo Meggiorini.
The former Inter man capitalised on a mistake from Fredy Guarin to level the scores before firing Torino ahead after the break.
It fell to Esteban Cambiasso to rescue a point for the hosts, with Stramaccioni left wondering what might have been.
He told the club's website: "We started out really well and our aim was to keep Torino from playing the game they wanted to play.
"We went ahead but then they were playing better than we were, although I don't think they created more.
"Then came a collective error on our part. It's a general regret because the mistakes are always team errors.
"Why do I call Guarin's mistake a collective error? Because I don't like handing all the blame to one player, and it was also a mistake on the part of the entire defence.
"Myself, the keeper and Guarin - we all deserve our share of the blame. We threw away a lead."
Stramaccioni does not have to pester club president Massimo Moratti to bring in quick replacements for Wesley Sneijder and Philippe Coutinho, with the latter expected to join Liverpool later on Monday.
"I don't have to convince anyone," he added. "The situation is very clear - our team has its own identity and things are going very well as they are.
"Our goal is reaching third place, regardless of whether any new arrivals come in. The league standings are very close and today we blew a chance.
"But at the same time I have to give my compliments to Torino."
Torino look to be putting fears of a quick return to Serie B to one side having climbed to 12th on the back of a run of six games without defeat.
Head coach Giampiero Ventura told gazzetta.it: "We are newly promoted. We must always remember that.
"Sure, we are plotting our own course in Serie A and we are improving one step at a time.
"We need to secure our survival as soon as possible, then we can think about climbing the league table."