The midfielder, who made his first appearance since Boxing Day in the 3-0 loss, feels the in-form Toffees took advantage of the Gunners' susceptibility to breakaway goals
The Gunners were second-best at Goodison Park as Roberto Martinez's in-form side stormed to a 3-0 triumph to move just a point behind Arsene Wenger's men in the battle for Champions League football.
Ramsey has called on his club to bounce back in strong fashion, starting with next weekend's FA Cup semi-final with Wigan and remains confident of claiming a top-four finish.
"We are really disappointed," the Wales international told the club's official website. "It was a massive game - there was a lot riding on it but we conceded some sloppy goals.
"We were quite vulnerable on the counterattack and they exploited the opportunities. I thought we started quite positively. We had a few attempts and got into dangerous positions, but you can't concede goals like that.
"We have to pick ourselves back up now. We have still got a lot of points to play for. We are in the semi-final of the FA Cup so we have got to put things right.
"We have to put a strong run-in together now. We have five games left and we will aim to win them all to give us the best opportunity to finish fourth or higher.
"I think Everton still have a few difficult games but then again every game is difficult in this league. So many teams can upset each other so we will have to be aware of that, concentrate on ourselves and just play for the remaining 15 points."
Ramsey made his first appearance since Boxing Day against Everton, having endured a lengthy lay-off due to a thigh injury, and is thrilled to be back in action as Arsenal look to finish the season on a high.
The midfielder added: "It was very frustrating for me to be out for three months of the season when things were looking so good.
"These things happen in football and I am just glad to be back out there now. Hopefully I can show what I can do, help this team achieve Champions League football again and hopefully have a medal at the end of the year."