There is always more than one way to skin a cat.
Another washer and a good torquing with pliers certainly will do the trick.
The good thing about Teflon tape is that one roll will address multiple leaks, whereas one washer will only address one leak.
If you look at a hardware store, you will probably see a white roll with either a red or blue cover. They are identical, except one has more tape. There is also a yellow roll, with yellow tape. It is used for sealing natural gas threads. This tape is thicker than the white Teflon tape used for water.
When you put the Teflon tape on, hold the male threads in one hand, with the male threads facing you. Then apply the tape in a clockwise manner. That way, when you then go and screw the pipe into the female portion of the fitting, the action of screwing it in will tend to keep the tape on the threads.
Another benefit of using Teflon tape is that it helps prevent the threads from corroding/locking up after prolonged periods of time.
Also, rubber washers can deteriorate over time, especially when exposed to hot water.
I have not yet seen Teflon tape deteriorate over time, although I am open to correction on this point.
But again, congratulations on fixing your leak.