Neither side could find a breakthrough in normal time, meaning Tuesday's match was decided by penalty kicks at FedEx Field in Maryland, and it was United who emerged 5-3 victors.
Despite that setback, Inter boss Mazzarri was more than happy with the application of his team in what he considered an even contest.
"It went very well for us," he said.
"It was a balanced game and I liked the team's attitude."
Vidic was handed a fine reception from the United supporters who were in attendance when he replaced Marco Andreolli 10 minutes from time and Mazzarri was delighted with the warm welcome afforded to the Serbian.
"It's a pleasure to see these kinds of things," he added. "They're really good for football. It was a great event to watch."
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