The Magpies had two goals disallowed at St James' Park as they were held by their Ukrainian opponents in the first leg of the last-32 tie.
"We're absolutely gutted," Taylor told Sky Sports News.
"The gaffer has just made the point to us that we should be 2-0 ahead. We had those two goals chalked off; we're disappointed with that.
"It was one of our best performances in a while. Everything the gaffer asked of us we did, we just didn't win."
Newcastle travel to the Ukraine to play the return leg on February 21.