It is not just your chest which is activated during the bench press.

Your shoulders and triceps are used too, and your shoulders especially can suffer if you aren't benching correctly.

You want to tuck your elbows in, rather than having them spread out wide. Out wide will force most of the pressure onto your shoulders, rather than your chest.

Try and create a mind-muscle connection with your chest, and aim to bring your arms together, rather than pushing straight up. This will ensure you activate your chest the most.