At what point does it become my trash (see details)

Suppose I’m walking along and I see a discarded paper cup on the ground. I pick it up, thinking that I’ll throw it into the next trash can I see. But I walk and walk, no trash can in sight, and finally I get sick of carrying the damned thing. If I put it back on the ground, have I littered? Is my ethical responsibility more engaged by having picked it up than if I had noticed it lying there and just left it?