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The rare apology follows Apple's launch of its own mapping service earlier this month, when it began selling the iPhone 5 and rolled out iOS 6, the highly anticipated update to its mobile software platform.
Users complained that the new Maps service - based on Dutch navigation equipment and digital map maker TomTom NV's data - contained geographical errors and gaps in information, and that it lacked features that made Google Maps so popular from public transit directions to traffic data and street-view pictures.
"We are extremely sorry for the frustration this has caused our customers and we are doing everything we can to make Maps better," Cook said in a letter to customers released on its website, adding that the company "fell short" of its commitment to deliver "the best experience possible to our customers."
Unusually, he suggested that customers download rival mapping services available in Apple's App Store while the company improves the product.
"While we're improving Maps, you can try alternatives by downloading map apps from the App Store like Bing, MapQuest and Waze, or use Google or Nokia maps by going to their websites and creating an icon on your home screen to their web app," he said in the letter.
Apple is typically loathe to tout rival services and the contrite apology by Cook is an indication of how Apple is changing under the chief executive who took over last year from co-founder Steve Jobs just before his death. It also took the additional step of prominently displaying the rival services on its Apps Store.
"It is a bit unusual but at the same time, Tim is keeping Apple's commitment to provide the best user experience for customers," Sterne Agee analyst Shaw Wu said. "A key reason for Apple's success is keeping customers happy so we think this is a good move."
"People forget that Google Maps started out inferior to Mapquest and Yahoo Maps," he added.
Apple's home-grown Maps feature -- stitched together by acquiring mapping companies and data from many providers including Waze, Intermap, DigitalGlobe and Urban Mapping -- was introduced with much fanfare in June by software chief Scott Forstall. It was billed as one of the key highlights of the updated iOS6 software.
But errors and omissions in the maps service quickly emerged after the software was rolled out, ranging from misplaced buildings and mislabelled cities to duplicated geographical features.
The last time Apple faced such widespread criticism was in 2010, when users complained of signal reception issues on the then-new iPhone 4 model.
A defiant Jobs at the time rejected any suggestion the iPhone 4's design was flawed, but offered consumers free phone cases at a rare, 90-minute press conference called to address those complaints.
While Apple fixed the issue, Jobs had apologized to users only after he was specifically asked if he was sorry. He also said the issue was shared by all the major manufacturers, naming rivals Research in Motion , Samsung Electronics and HTC Corp.
Cook himself played a key role in convincing Jobs to tackle the negative publicity that arose around that issue, something he was initially reluctant to do, according to his biographer.
"Finally Tim Cook was able to shake him out of his lethargy," Walter Isaacson said in his biography on the late Silicon Valley icon. "He quoted someone as saying that Apple was becoming the new Microsoft, complacent and arrogant. The next day Jobs changed his attitude."
It remains to be seen how fast Apple can fix the mapping glitches. Jobs had been in a similar position when he allowed email synchronization software MobileMe to launch in 2008, to deadly reviews. The mercurial CEO took the group to task for it and replaced the group's head. The service is now folded into the iCloud product.
Mapping is a complex process that takes a lot of resources and years to perfect, said Marcus Thielking, co-founder of Skobbler, maker of the popular GPS Navigation 2 app, built using the crowdsourced OpenStreetMap platform.
"It helps a lot if you have great data to start with," he said, adding that it appears that different database were thrown together in building Apple Maps. "They (Apple) can offer incremental updates and that's what they will do."
Cook said that more than 100 million iOS devices are using the new Apple Maps and that the more people use Maps, the better it will get. He also offered some hints on why the company decided to remove Google Maps.
Apple launched the Google-powered Maps "initially with the first version of iOS" and created a home-grown version of the service as it wanted to provide more features, Cook said.
"As time progressed, we wanted to provide our customers with even better Maps including features such as turn-by-turn directions, voice integration, Flyover and vector-based maps," he said in the letter.
Google provides turn-by-turn navigation on Android-based devices but the popular feature was not available for Apple devices. Apple Maps replaced Google Maps in iOS 6 and the Google service is now only available through a browser.
Shares of Apple fell 2 percent to close at $667.10 on Nasdaq.