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."
The match pitted new Inter centre-back Nemanja Vidic against his former side for the first time since he left Old Trafford at the end of last season following the expiry of his contract.
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."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
