Apple's new Maps tool replaced Google Maps as the pre-loaded service on newer iPhones, iPads and the iPod Touch last month.
But users quickly started reporting inaccuracies and complained of poor quality maps compared with Google's service.
In an interview this week at the 92nd Street Y in New York with AllThingsD's Walt Mossberg and Kara Swisher, former Google chief executive Schmidt said that Apple "should have kept with our maps" as they are "better".
Schmidt would not be drawn on reports that Apple was concerned Google was keeping features, such as turn-by-turn navigation, exclusive to its own Android operating system.
But he did say: "We negotiated all of these details with Apple, and the fact of the matter is they had decided a long time ago to do their own maps."
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Schmidt said that Apple has learnt that "maps are really hard" and take time and investment to produce.
"We invested hundreds of millions of dollars in satellite work, airplane work, drive-by work to get the maps accurate. And we think we have the best product in the industry," he said.
"Apple has done extremely well during the last five years," said Schmidt, before adding: "Actually, Apple has done very well using our maps."
There have been reports that Google is to launch a native iOS app for Google Maps, as it has done with YouTube after Apple also dropped that service as a pre-loaded option on its operating system.
Schmidt noted: "I don't want to pre-announce products. But I can tell you that were we to do that, they would also have to approve it. They haven't approved all of Google's offerings over the years."
However, he added: "Apple and Google are two large and important institutions. We are always in negotiation, which makes for a structurally stable outcome."
Schmidt feels that Apple's Maps will improve going forward as the company addresses the criticism and invests in the service.
"Apple has clearly made the decision to do their own maps. They made that decision a long time ago," he said.
"I think we should assume that they will continue to make their maps better and address the criticisms that exist."
Following the Apple Maps debacle, Google Maps is now a major selling point of the Android operating system.
Schmidt was proud to say that 1.3 million smartphones are being activated on Android every day, far more than for the Apple iPhone.
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