Newcastle have not won a major trophy since 1969 and Taylor is keen to see the club do well in the cup competitions this season.
Alan Pardew's side entertain Manchester City in the fourth round of the Capital One Cup on Wednesday and Taylor feels Newcastle have a squad capable of progressing to Wembley.
"Obviously we aren't in Europe this year so we have to make sure we do well in the League Cup and the FA Cup," said Taylor in the Evening Chronicle.
"That's what we're trying to do. We must stand our ground in that. The last few seasons we have been a bit sloppy in certain games. We have to take the cups by the scruff of the neck and do well in them."
Asked if Newcastle should play a strong team, Taylor said: "I'm sure that is what the manager will do.
"We want to do well in that. We talked about it at the start of the season and we want to do well in the cups.
"We look at Swansea and Bradford doing well.
"We'd like to follow that. With the players we've got there should be no reason why we can't. We have to play well as a team and hopefully get the stroke of luck we need too."