The defeat leaves Alan Pardew's men with a lot of work to do in next Thursday's return leg if they are to claim a semi-final spot, and Taylor admits they were guilty of some "sloppy" play in Lisbon.
But asked if Newcastle could turn the tie around, the 27-year-old said: "Too right there's a belief we can do it. There's no reason why we can't win the game next week. We can cause them problems, get in their faces and not let them have time on the ball."
He added: "Up until the second goal, we were on top. We didn't let them have many chances and we took the game to them.
"We got right in their faces, and you could see them getting a bit angry. There were a few daft tackles from them.
"When Papiss (Cisse) hit the post, it could have been different.
"We proved that we could win this tie, but a couple of sloppy goals gave them the advantage. You can't afford to do that."
Regarding the incident that resulted in the penalty - which Oscar Cardozo scored twice, having to retake due to encroachment first time around - Taylor said: "It just hit my hand.
"There's nothing I could do, I couldn't get out of the way. The guy behind the goal gave it."
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