Arsenal were second-best at Goodison Park as Everton stormed to a 3-0 triumph and boosted their chances of earning fourth place in the Premier League.
Roberto Martinez's men are now just a point behind Arsenal in the battle to secure UEFA Champions League football and the Merseyside team also boast a game in hand.
Ramsey has called on his club to bounce back in strong fashion, starting with next weekend's FA Cup semi-final with Wigan Athletic, and remains confident of claiming a top-four finish.
"We are really disappointed," he told Arsenal'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 counter-attack 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.
The Wales international is thrilled to be back in action, and is hopeful of helping Arsenal achieve their remaining targets this term.
He 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."
