Despite losing Thursday's quarter-final first-leg contest at the Estadio da Luz 3-1, United began the match well and took the lead through Papiss Cisse's 12th-minute goal.
Striker Cisse also hit the post with the score at 1-1 before Benfica, who have been beaten only once at home all season - by Barcelona - and have scored over 100 goals in the campaign, took control of the tie.
However, when asked if Newcastle could turn the tie around in next Thursday's second leg at St James' Park, 27-year-old Taylor 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."