You can try the Pitch Correction plugin. One method would be to duplicate the track and instanciate the plugin on just that track. Use the scissor tool to cut and isolate the area(s) of bad pitch and move them to that track. In the best case you'll find a setting for the plug that takes care of all of the problematic regions. If not, create additional duplicates of the track, move each problem region to its own pitch-fixit track, and adjust the individual plugins accordingly.
Another option would be to use a 3rd party plug such as Melodyne, where you can draw/edit correction to pitchy areas.
Back to Logic, there's also the Pitch & Time machine (sample editor) which can be used to adjust pitch (and not time). It'll take you a minute to learn how to use it if you're not already familiar with how it works. And it's a destructive operation, so if you go with this option, be sure to make a backup of your original audio file just in case you're not 100% happy with the result.