I will be explaining what I think:
A battery acts like a pump which provides energy to do work on negative charges to move them towards the negative terminal, and hence creating an electric field. Now, due to this field, when a wire is connected to make a circuit, electrons move from negative to positive terminal, thereby making electric current. Now, if I put more and more resistors in the circuit, the electrons will have to do more and more work. Let me explain in more detail: Suppose there is only 1 resistor. Then, electrons will flow through it, they will loose some of their energy(to produce some desired effect like light or heat), but, because they are under the influence of the electric field, they will again gain some more energy. Now, if I add more resistors, the activity will be the same. Electrons will loose energy, and then again gain some through the electric field. Then, why does a battery drain faster in more resistors? Battery is just pumping charge from positive to negative terminal, what else is it doing? Why does it drain quicker?
(For good explanation, viewers can consider resistors to be bulbs)
NOTE: Resistors are being added in series!