The Gunners arrived in Turkey four days after their shock defeat at home to Aston Villa but cruised to victory thanks to second-half goals from Kieran Gibbs, Ramsey and Olivier Giroud.
It puts them in pole position to make the group stages of Europe's elite competition ahead of the second leg next week and Ramsey told Sky Sports: "It wasn't the ideal start to the Premiership but we bounced back tonight.
"We played really well as a team. We've been under a lot of criticism of late but it was vital that we stayed switched on and got a great result here, which we did.
"We look very comfortable now going back to the Emirates for the second leg."
It will go some way to relieve some of the pressure on the players and in particular the manager Arsene Wenger who was booed at the Emirates on Saturday.
But ahead of next Tuesday's second leg, striker Theo Walcott maintained an air of caution.
"It felt like, with the tempo of game, we dominated it in the centre of park and if we kept on going at a high intensity we'd get a goal, and we did that," he said.
"It was three great goals and it's a great result going to the Emirates now on Tuesday night.
"Its nice and comfortable but we've got to be professional on Tuesday. They're going to want to come and make it up to the fans for tonight and we have to be ready for that."