When the tyre of the cycle is inflated, the pressure inside the tyre is reducing the normal force between tyre and the ground, and thus reducing the friction between the tyre and the road. When the tyre gets punctured, it gets deformed during the rotation of the tyre, the energy supplied is used up in changing the shape and not overcoming the friction, and due to deformation, friction increases. Therefore we have to apply more force in order to move the cycle.