And that has led to some disappointment for people who helped set the city’s sights so high.

“The hype has definitely died down,” said David Tisch, an investor and a co-founder of Techstars, a start-up incubator in New York, where he was formerly a managing director. “It’s harder to point to one thing and say, ‘that’s New York tech.' ”

Some companies have come close to breaking out, but hit one bump or another.

Tumblr, the blogging service based in downtown Manhattan, made headlines last May when Yahoo acquired it for $1.1 billion. But the sale, widely considered a major moment for the city’s tech scene, was also seen by many as a Hail Mary play because the company was struggling to turn itself into a successful business when the deal went through.

Fab.com, an online retailer, once looked as if it could be the next Amazon. But in the last year, it has lost top executives and has struggled to keep its financial footing.

Even Foursquare, the location-sharing app that gained widespread attention a few years ago and was often the subject of acquisition rumors, has faded a bit from the spotlight. The company recently said that 45 million people had downloaded its application, but Foursquare would not release active user numbers.

Some prominent New York investors who had been bullish on the city and local start-ups have started to look beyond its borders. Fred Wilson, for example, a partner at the Manhattan firm Union Square Ventures, said he had been putting more money into other markets, including Europe and Canada.