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The Gunners went in behind at the break before the Welshman and a late Olivier Giroud effort ensured they progressed in the competition.
And when asked whether Wenger was harsh in his assessment of the team after 45 minutes, Ramsey was quick to state that the players knew their performance hadn’t been up to scratch.
He said: “No. We all realised that wasn’t good enough for us, for this club.
“So it was important for us to go out there and give it a good go in the second half and we did that.”
Ramsey was also delighted to get on the scoresheet and believes Preston should be proud of their efforts.
He added: “I’ve played in the Championship and I know how difficult every game is.
“They proved that in the first half and it took us by surprise. The level of commitment and effort, we didn’t match that.
“Second half we needed to have a different attitude out there and I think we showed that.
“Obviously it was nice to score, to get on the scoresheet finally.
“That gave us a bit of momentum to go forward and win the game from then on.”
Arsenal’s next challenge is a Premier League match with Swansea next weekend as they look to keep up their title challenge.