The Gunners strengthened their hold on fourth place and Champions League qualification, as goals from the Wales international and a brace from Lukas Podolski handed them the win over Steve Bruce's side.
Ramsey told the club's official website: "I thought it was a very professional performance from the lads. It was important to come here and get the win to keep our position in the league. I thought we did ever so well today.
"It was always going to be a tough game coming here. Any result away from home in this league is good. We were professional in the way we went about things but we got the job done.
"We stayed quite tight at the back and we got the job done on the break and made them pay."
The Gunners hold a one-point lead over Everton in fifth in the battle for the final Champions League place.