You don't need to feel the burn, but a lot of people, myself included like that feeling at the end. I usually close out a muscle group with some sort of burn set, drop sets work great for this.
But as mentioned, check your form. You could be doing it without engaging your chest as much as you should be.
When you bench :
Are feet flat or tucked back?
Is your back flat or arched?
Shoulder blades retracted back?
Elbows point where? Out in line with bar, or in towards feet, or in between?
Bar touches what part of your chest? Above or below nips?
Hands are where on bar? Out wide, shoulder width, slightly more or less?
Survey over. Answer those for a better explanation. No charge..