Sneijder was withdrawn midway through the second half and made his displeasure known by walking straight down the tunnel rather than joining his team-mates on the bench.
Inter went on to win the game with goals from
He said on Twitter on Monday morning (Italian time): "Great victory yesterday!!
"Was a bit angry, because I want to play everything... Not because I have a problem with the coach. But I know there are many games to play... Preparing for Thursday ;)."
Stramaccioni preferred to focus on his team's second away win of the season and confirmed Sneijder's theory that the player was merely frustrated at being withdrawn.
"It's a normal reaction, he'd like to finish every match," he said on www.inter.it.
"Sneijder is a key player for us but he'd played two games in a row and had racked up lots of minutes on international duty.
"And that was Torino's best period so I wanted to send out a message by bringing on an out-and-out striker.
"We're a well-knit side and we're working well together. We're determined to achieve things but we want to let our football do the talking on the pitch."
Stramaccioni felt the introductions of Cassano, and in particular
He added: "There was a spell during the second period when we were losing the ball in dangerous positions - at that stage the game had taken a slightly different turn. Then when Gargano came on we managed to get a grip of things again.
"Perhaps there were a few tired legs out there but that's understandable because it was a huge energy drain.
"It was important for us to get another win under our belts after the blip last time out, so that we could stay up there just three points off the leaders. This was a big win for us."
Napoli coach Walter Mazzarri has announced his decision to leave the Serie A runner-up after four years at the helm.