Stramaccioni oversaw the Nerazzurri's second home defeat of the season, with second-half goals from Simone Vergassola and Francesco Valiani giving Serse Cosmi's side a convincing victory.
Nevertheless, the 36-year-old expressed his "great confidence" in his playing staff, despite now going on a run of five home games without victory so far in 2012-13.
"The defeat was bad. Now we must not lose faith in what we are doing. We have built a lot, but we were unable to find the goals," Stramaccioni told Sky Sport Italia.
"A defeat should not affect our work. [We were on] a fresh start in the second half, [but] Siena hit us. Now is the time to remain united. I have great confidence [in the players].
"We must not concede an inch. Today was the Inter who created more. Until the goal of Vergassola, Siena were only dangerous from corners. We are a new team, we have to find the right balance."
Inter travel to Chievo on Wednesday for their next Serie A fixture.