With the release of iOS 6 this week, the US technology giant upset users by dropping Google Maps in its mobile operating system in favour of its own proprietary system.
Alongside being rolled out on certain existing Apple iPhones, iPads and iPod Touch devices, the Maps app also comes preloaded on Apple's brand new iPhone, which went on sale today.
But there have already been various complaints about Apple Maps, including inaccuracies, misplaced towns and cities, and key landmarks being missing.
Apple said that it appreciated the feedback from customers and was working on improving the Maps software, which was created with help from navigation firm TomTom and others.
In a statement, Apple spokeswoman Trudy Muller said: "Customers around the world are upgrading to iOS 6 with over 200 new features including Apple Maps, our first map service.
"We are excited to offer this service with innovative new features like Flyover and Siri integration, and free turn-by-turn navigation.
"We launched this new map service knowing that it is a major initiative and we are just getting started with it. We are continuously improving it, and as Maps is a cloud-based solution, the more people use it, the better it will get."
The problem facing Apple is that Google has spent years building up its database of mapping information, including local data, satellite imagery and the Street View project.
Apple users have now lost all of this and it will take Apple some time to build up a similar wealth of information.
Users took to Facebook, Twitter, Tumblr and other social media networks to mock the failings of the mapping application, including whole towns, such as Stratford Upon Avon, being missing on the service.
Maps is also considered very poor at locating local businesses, a real area of strength for Google Maps.
Muller said that the firm was collaborating with developers to integrate existing transit maps into the service to improve its accuracy.
"We're also working with developers to integrate some of the amazing transit apps in the App Store into iOS Maps," she said.
"We appreciate all of the customer feedback and are working hard to make the customer experience even better."
Various technology websites have also noted that Apple has placed lots of job adverts for mapping experts, indicating that it knows this is an area that more has to be done to to ease its customers concerns.
There is currently no Google Maps app available on the App Store, but Google's system can be accessed through the phone's web browser and Google is thought to be working on a dedicated iOS app.