James McClean described the Republic of Ireland's defeat to Sweden as gut-wrenching after the visitors fought back for a 2-1 success at the Aviva Stadium.
Ireland were ahead thanks to Robbie Keane's strike but Johan Elmander and Anders Svensson netted to deny Giovanni Trapattoni's men.
McClean told RTÉ: "It is a slim chance but we still have a fighting chance. We have to fight until the death. Hopefully other results go for us, stranger things have happened. We have to keep a lot of hope.
"Looking at the first half an hour I think we deserved the lead.
"But once we went 1-0, we kind of killed ourselves a bit. Instead of going for a second, we sat back a bit and you can't do it against quality teams like this.
"It is a bit gut-wrenching to be honest."
Richard Dunne also refused to give up on qualification.
Dunne believes there is still a glimmer of hope and told Sky Sports 2: "It's a big blow tonight.
"We wanted four points from these two games but it's been a close group all the way through.
"Hopefully somewhere this week we will step up.
"It's very difficult now but we have to keep going, there are three games to go.
"We have just got to be proud and make sure the fans are proud of us."