Headlights were on all night - Battery died

I accidentally left my car's headlights on all night and the
battery died! Triple A jumped my car but tried telling me
that I would need to get my battery looked at and possibly
spend another $120 to get a new battery. I know with
phone batteries if your phone dies too many times it hurts
the max amount of power it can hold. I assume it is the
same with cars, but the man tried telling me I needed a new
one after one time. Will my car be fine with the same
battery or should I get the battery looked at /replaced? It's a
new battery that was put in less than a year ago.