Manchester City striker Edin Dzeko netted either side of the break to put the Bosnians in control in Missouri, before Didier Drogba found the net in second-half stoppage time.
And, after expressing his delight with an impressive victory, Susic allayed fears surrounding Sead Kolasinac, Emir Spahic and Ognjen Vranjes, who all came off with knocks during the match.
"I congratulate my players for their victory against a good team," he said. "I think we played well and deserved to win.
"When it comes to injuries to Kolasinac, Spahic and Vranjes, I can say that none of the injuries was of a serious nature, as I was informed by a doctor, but we did not want to take the chance and I am convinced that everyone will be able to continue."
Susic also reserved special praise for defender Muhamed Besic, adding: "I've always followed his game and never doubted his quality.
"He's advanced in all areas and will be a major player for a long time."
Susic's men start their Group F campaign against Argentina on June 15.
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