The Hammers' six-match unbeaten run in the Premier League came to an end courtesy of Ryan Giggs' individual goal in the second half.
But West Ham matched the leaders for long periods, with Carlton Cole having his side's best chance in the first half when his attempted chip was saved by Edwin van der Sar.
Zola was happy with how his team restricted the opposition's chances and believes it is an indication of the progress being made at Upton Park in recent weeks.
Good sign"I think it's a good sign, for certain, because it has been a close game," Zola told Sky Sports.
"I believe that our goalkeeper made only one save, so I think it was a close match.
"That's the difference when you play the best team in the world, if you make one mistake you pay and it's costly.
"I'm very happy with the performance of my players. It was a tough match and they stood up to Man Utd in a very good way."
The West Ham boss did not want to criticise Cole, who has been called up to the England squad to face Spain, for not taking advantage of his team's best opening.
Zola added: "He wanted to chip it over and maybe he should have gone for power, but to be honest he has played a great match.
"I can't say anything to him and in the second half there were a couple of chances where we were close."
The Italian continued: "I don't just see the defeat, I see the way the team plays and they stood up to the best team in the world right now and they played just as well as them."