Arsenal last failed to play in the Champions League proper in the 1997/98 season and head into Wednesday's first leg against Fenerbahce on the back of a 3-1 home defeat by Aston Villa.
Arsene Wenger is also facing supporter unrest following Arsenal's failure, so far, to strengthen their squad during the summer transfer window.
Meireles is expecting a close encounter and he hopes Fenerbahce can still be in the tie for the trip to Emirates Stadium for the second leg next week.
"The pressure is on Arsenal and that gives us a little advantage in a game which is 50-50," the former Liverpool and Chelsea player is quoted in the Daily Mirror.
"Arsenal are difficult opponents but we're also a tough opponent for them. This tie will be very level, very well matched.
"Arsenal's defeat to Aston Villa was a surprise but it's not good for us. They will be even more focused and determined for our game.
"Our key is to go to London with a tight scoreline. I've had some good experiences in London and I believe if the result is within reach then we can go through."