Lasse Schone's strike in the 51st minute left the Scottish champions bottom of Group H with three points from four games ahead of the visit of AC Milan and before their final fixture against Barcelona in the Nou Camp.
Ajax moved into third place with four points and will have the better of Celtic if head-to-head comes into the equation, with Milan on five points and the Catalan giants already qualified on 10 points following their 3-1 home victory over the Italians.
Kayal, pointing to last season's last-16 achievement in the competition, was keen to stress that a win over the Rosseneri at Celtic Park will revitalise qualification prospects.
"We always believe we can do something," the Hoops midfielder told BBC Scotland.
"We don't want to just say we are in the Champions League, we proved that last year and we want to prove that this year also.
"The manager gave us the belief and we still believe. Everything is possible.
"Just looking to the next game, it's going to be tough. Celtic Park is always hard for every team.
"We'll try to do the best and hopefully we can win the game. With six points in the group, it would put us in a good position."
Mikael Lustig took a more pragmatic approach to the next two Champions League matches.
The Hoops right-back acknowledged that the game against Ajax was not one of Celtic's most competent European performances and when asked about qualification chances, he told BBC Scotland: "Of course it is possible but it is really hard.
"We need to win against Milan and get points in the Nou Camp so it will be hard.
"First of all, we need to find a way to score goals.
"We have confidence playing at Parkhead, both games against Barcelona and against Ajax were quite good so hopefully we can still do it.
"It was disappointing against Ajax. We felt we had a really good chance to take points from this game but we didn't.
"We need to learn to score. We couldn't handle the ball in the first half.
"We did quite well in defence but when we got the ball we just gave it away. So we need to do better on the ball. We had some decent chances in the second half but didn't score.
"We have created a lot chances, probably more chances than we did last season. We need a little bit extra, we need someone who can score."
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