The Nerazzurri have one foot in the play-off round following after easing past the Croatian club at the Stadion Poljud following goals from Wesley Sneijder, Yuto Nagatomo and Philippe Coutinho.
It was Inter's first official match of the new season, but Stramaccioni does not think that his players were feeling the pressure.
"We were not nervous, just very focused," he told the club's official website. "We prepared for this game in minute detail.
"Look at the fans here and that is after losing 3-0; imagine what it would have been like if we had lost 3-0. Hajduk might have been fitter than us but I think Inter played the perfect game tonight.
"We are keeping our heads down. It is a good result but what I liked was the fact that we never stopped trying to play football and we gave very little away.
"It is a shame about Matias Silvestre's mistake at the end, otherwise Samir Handanovic would not even have touched the ball. We are happy but we will move on and keep our feet on the ground."
Stramaccioni was thrilled that Inter got off on the right foot after the club finished in sixth position in Serie A last season.
"We are working well together and we are a close-knit group, both on and off the pitch," the 36-year-old coach said.
"We also had a surprise visit from the president today. It shows that Inter are united, compact and determined to let their football do the talking."
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