Taylor says Newcastle must be considered serious contenders for the competition they last won in 1969. They face Anzhi Makhachkala or Hannover of Germany if they get through.
Taylor said: "We know we are under pressure in every game we play. We want to do well in this competition. The gaffer has made it clear in team meetings and the players know too.
"I am desperate to win something. Hopefully this could be it. People say we have been playing weakened teams but we haven't been playing weakened teams. We have got great players in our squad and we have to try to do as well as we can in every match we play.
"There is more European experience in the squad now with the signings we made in January and we do have the young players that are good enough."