The Nerazzurri coach felt his side could have played better against the Rosanero, but was also quick to deny that Wesley Sneijder was left out because of his contract dispute
An own goal by Santiago Garcia in the 74th minute ultimately separated the two sides, despite the Rosanero putting in a brave performance.
And Stramaccioni admits his side could have produced a better display.
"At times like this, when we're not at our best, I like the attitude of the team and the consistent performance," the trainer told reporters.
"We gave everything and created some clear-cut chances, but we faded somewhat in the second [half].
"The goal made everything easier, especially with our forward line under so much pressure," he added. "Palermo leave very little space, but with [Freddy] Guarin we had another option."
When asked about Wesley Sneijder's position at the club, the Inter coach continued: "Being coach of Inter involves working on the pitch and away from it, just like any team. It's my job to pick the best team available, and at the moment I'm not picking him.
"This has nothing to do with his contract, I have to select the team and Inter come first. It's not a case of the president [Massimo Moratti] telling me not to pick Sneijder, I pick the team."
Javier Zanetti echoed his coach's view, saying: "Fortunately we scored a goal which allowed us to grab the three points. We tried everything we could to win what was a very tricky contest."
Inter are currently in third place, four points of adrift of Serie A leaders Juventus, and face second-placed Napoli next weekend.