Is it normal to kill animals that carry diseases such as Mice and Rats?

For example this one day I was in the Subway system in NYC on 34th St Herald Square waiting for the C Train to come after work while charging my phone and I literally seen a Subway Rat running around in the it and killed it and casually walked away.  By the way neither the Mouse or the Subway Rat was Bleeding after I killed them. ( Most likely because like my friend they was most likely dehydrated )  Is this Normal and why or why not??
Answers

Ludwig

I think you are wrong. When I visited the USA I stayed in New York for over a week, and saw many of the animals that live in the Subways. I was told that they are Possums, and a protected species.