It's interesting how money clouds people's judgements. I don't see the counter-offer as offensive, I would take it as a compliment that they really wanted to keep you(of course it stings to know that you were probably underpaying you while you were there, but that's how businesses work they pay you just as much as your worth).

Also, you should always negotiate when you get a job offer. Remember the employer has tons of expenses to have you there and a few thousand more per year is relatively little to them, but significant to you, the worst they can tell you is that's the best they can offer. Any employer that would take offense at an attempt to negotiate is not worth working for.