Papiss Cisse twice had goals ruled out for offside, with replays suggesting at least one of them should have stood.
"We're absolutely gutted," Taylor said after the goalless draw.
"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."
Despite failing to find the back of the net, Yohan Cabaye believes not conceding an away goal gives Newcastle an advantage heading into the second leg.
"It was a tough game. The important things is we haven't conceded a goal," he said.
"If we are doing the right thing away from home, we score, then they have to score two.
"That's the main thing from tonight."
Taylor is also confident Newcastle can score an away goal in the Ukraine.
"Tonight showed we have goals in us," he said. "We can go there with more confidence than them. We will hope to pose them more problems."