Rubin's Alexander Ryazantsev converted Bebras Natcho's saved penalty after Jonathan had fouled Gokdeniz Karadeniz, with young striker Marko Livaja equalising with a header and registering his first senior goal in the process.
But Jose Salomon Rondon capitalised on slack defending to strike what appeared to be a shock winner before Yuto Nagatomo rescued Inter deep into stoppage time.
Stramaccioni told the Gazzetta dello Sport: "Inter pleased me in the second half, they pushed on, so much so that Rubin ended up with five at the back and four in midfield, with only Rondon in attack.
"So it was sort of ironic that it was him who punished us for our lack of concentration.
"It's annoying not to get a home win because we wanted to give joy to our fans, who backed us all the way through.
"My analysis is straightforward - we were punished for two mistakes."
Croatian teenager Livaja was delighted to score his first goal for the Beneamata but rued his team's failure to push on and seal victory.
He said: "It was a great game, Rubin are a good side and they were hard to play against.
"I'm really happy to get a goal at home, but we hope a win will come soon, hopefully against Siena on Sunday.
"I thank the coach for putting his faith in me. He told me not to sign for Espanyol but to stay here where he promised me a lot of playing time.
"I hope it continues."