The Magpies, taking on a side who had been beaten at home only once all season - by Barcelona - and netted more than 100 goals in the campaign, started the quarter-final first-leg contest at the Estadio da Luz well, with their early attacking intent being rewarded when Papiss Cisse's close-range finish put them 1-0 up in the 12th minute.
Cisse had a deflected effort turned against the post by goalkeeper Artur 11 minutes later, but within two minutes the Portuguese league leaders equalised as Rodrigo slammed home from Tim Krul's parry.
The upright denied Cisse again in the 47th minute when he chipped Artur and substitute Lima then put the hosts 2-1 up in the 65th minute having intercepted Davide Santon's poor attempted back pass, with Oscar Cardozo converting a penalty six minutes later after Taylor was penalised for a handball.
It 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.
"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 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."
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