A TL081C has a max input offset voltage of only 10mV and a typical voltage gain of 200,000. So of course its output will be offset if there isn't any negative feedback to reduce the gain.
Opamps are usually used with plenty of negative feedback to set the amount of gain to a usable number, extend the bandwidth and to reduce its amplification of its input offset voltage.
The single opamp TL081 has pins for connecting an offset adjustment pot.
You can connect a pot to an input to feed in your own offset adjutment.
More expensive opamps are available with their input offset voltage laser trimmed to be very low.
What is your signal that is so low in level that the input offset voltage matters?