Alexnet is the simplest of the pretrained deep learning models, you might want to try others (resnet, inception, etc).
You might also not have enough images to get a good model, I don't know how many you have.
You might be experiencing overfitting, how went the training? A near 100% accuracy in training data with not that much in validation data would be a pretty strong indication of overfitting. You can avoid overfitting with image augmentation, dropout layers, etc.
Also, some problems have inherently ambiguous classes. A network to classify musical genders in song files might have a hard time in separating similar musical subgenders, for example. You might take some time to think if this is not your case. If it is, your network might not be "innacurate" at all, you problem is inherently difficult instead. The prediction class scores might give an idea of such ambiguities: 2 classes appearing with average-ish scores, indicating the image might belong to either.