When focusing on losing armpit fat, there are two things that you should keep in mind:

Include more cardio and general strength training to your routine
Pay more efforts on specific strength exercises.
To tone your armpit, the most important areas that you should focus on are your back and chest.

Some exercises that will help you reduce armpit fats are:

Lying chest fly
This will work for your chest and upper arms.

Direction: lie flat on the ground. Hold your legs up at an angle of 90 degrees. Use your core strength to balance your legs. Now lift a small weight with your hands. Start with keeping your hands to the side of your chest and then lift them up straight to your chest.

Pull-ups
This exercise will help you build muscles and burn fats.

Direction: pull yourself up by hanging on to something above you. Only use your hands to lift your body up.

Chest press
This will be for your chest and upper arms.

Direction: lie down straight on the floor. Hold light weights with your hands and keep your hands to the sides with the elbows at right angles. Now straighten your hands to the upward direction, straight to your chest.

Standing reverse fly
This exercise will strengthen your back and chest as well as the back of your upper arms.

Direction: hold weights on your hands and keep your hands facing forward. Now lean a bit forward by bending your knees, then lift your hands to the up-facing ceiling. Again bring the hands down and repeat this process.

Pulling weights
Toning your back is a must to lose fat near the armpit and this is the exercise that focuses more on your back.

Direction: lie down on the floor straight with your tummy facing downwards. Keep your hands straight to the sides and hold some weights. Now lift your hands, arms and chin away from the floor. Repeat this process.

Doing some of these strategic exercises, you will efficiently reduce your armpit fat and have a toned body that you have always imagined yourself as. The crucial ingredient in such a process is effort and willpower and I hope you master in them.