Zola turned home a Niall McGinn cross from close range after 53 minutes which proved to be the difference between the sides, but Langfield made a brave save from David Goodwillie that was equally important.
McInnes said: "It was a hard-fought win against a decent United team. They've got good attacking options, and it's not often Dundee United fail to score.
"The teams had a bit of respect for each other - both sides have a threat, but I think for the most part that was cancelled out.
"If the game was screaming out for a bit of quality, that was provided in the build-up to the goal.
"The chance for Goodwillie was the defining moment. It was a great save from Jamie Langfield, and it was the one time they cut us open from open play, and we did the same in the build-up to the goal.
"We took our chance, and they missed theirs."
Langfield's save from Goodwillie drew praise from the manager, who added: "It was a good save rather than a bad miss.
"Jamie is as good as any Scottish goalkeeper in the SPFL. He's been brilliant to work with and is a great lad in the dressing room."
Of Zola, the Aberdeen boss continued: "Calvin thrives on service, and he got good service for the goal. He was where he should be at the right time, and made the difference in getting the three points.
United boss Jackie McNamara admitted to a sense of frustration at the result, especially with the manner of defeat, as captain Sean Dillon appeared to miss the opportunity to cut out the cross from which Zola scored.
"Frustration really sums it up. The players are a wee bit down and we're trying to get their heads up," he said.
"Sometimes it's wee things like a loss of concentration that cost you the match and that was the case.
"We dominated the match and passed the ball well, and I don't think Aberdeen posed us many problems.
"If anything we can be critical of our finishing, although Jamie Langfield had a good save from David Goodwillie."
There were encouraging signs for the manager, though, and he believes that continuing to play in the right manner will see United move forward.
He added: "I was pleased with certain aspects of our play, and I think If we play like that we'll win, or certainly draw, more games than we lose. We're creating chances, which is the most important thing."