You have a couple of potential problems with using an unregulated
charger to maintain or charge a lead-acid battery. The first problem
is that if the battery attempts to draw more current than the
unregulated supply can handle you may overhead the transformer or
other components in the supply. If on the other hand, the supply can
supply more current than the maximum bulk charge rating of the battery
then you may overheat and damage the battery if it is connected to the
supply when it is not fully charged. The third problem results if the
supply can output a voltage higher than 13.8 volts and can also supply
the necessary charging current. The battery voltage will eventually
climb to the supply voltage (above 13.8 volts), continue to draw
charging current and boil the water out of the cells damaging the
battery.

To be safe, you really need to regulate the voltage at 13.8V maximum
AND limit the current to protect the battery and the charger. If you
also want to get a fast charge on a discharged battery then you need a
multi-state charger that will apply a higher voltage (about 14.5 V) at
a limited current until the battery is almost fully charged and then
switch to 13.8 V to top it off and maintain a "float" charge.

I expect your battery did not reach the no-load supply voltage because
the supply was not capable of producing that voltage at the trickle
current needed by the battery.