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."
‘If I was Bournemouth, I’d be thinking if they can get past Manchester City, there’s no-one to stop them winning the FA Cup for the first time ever’ Former England star believes the Cherries have the ability to make history
‘I wasn’t concerned I’d done anything wrong – I stated a fact. It was taken out of proportion and people have recognised that they misread the situation a bit’ Gary Lineker gives FourFourTwo his thoughts on BBC suspension for asylum seeker tweet
