When you say that you don't have an oxygen sensor do you mean that there is nothing in the hole where the O2 sensor should be?
If that is the case, yes, that will for sure make your car run like crap!
There are four O2 sensors on these cars and I'm assuming that the one that you noticed was an "upstream" O2 sensor... The two upstreams are the critical ones.
Make sure that you plug it in all the way when you install it.