I just installed a new faucet and drain assembly. I have a very small leak that I now realize is because I installed a drain that is for a sink with an overflow but my sink does not have an overflow. Is there something I can put over the holes on the drain assembly or do I need to purchase a different drain assembly?

I don't know what holes on the drain assembly you are talking about. I have hooked up many sinks with and without overflow holes and have had no problem. Plumbers putty under the aseembly in the sink and teflon tape on the pipes.

I just installed a new faucet and drain assembly. I have a very small leak that I now realize is because I installed a drain that is for a sink with an overflow but my sink does not have an overflow. Is there something I can put over the holes on the drain assembly or do I need to purchase a different drain assembly?

You need to purchase a drain for a vessel sink.(see image)./ Good luck, Tom