Palace started the match in confident fashion and came desperately close to taking the lead after eight minutes played, with the very first effort of the contest. Excellent work on the right flank from Jorgen Strand Larsen saw the Norway international move into a great position.
He picked out Evann Guessand inside the box with a smart pass, but his shot from six yards out was somehow saved by Zlatan Alomerovic.
Shortly afterwards, Strand Larsen went for goal himself, but his effort could only force a routine save from the Larnaca goalkeeper.
Despite enjoying the bulk of possession in the first half, the hosts were finding the opposition defence to be a tough nut to crack after that early flurry of chances.
That said, Oliver Glasner’s side did manage to create one more big opportunity shortly before the interval when Alomerović came to his team’s rescue again with an impressive stop to deny Tyrick Mitchell from edging Palace in front from close range.
With the visitors struggling to pose any threat themselves in the final third, it was up to the Eagles to attempt to take the game by the scruff of the neck in the second half.
The deadlock was almost broken before the hour mark when an excellent delivery from Brennan Johnson found an unmarked Ismaila Sarr, but his header was slightly mistimed and lacked conviction, resulting in the ball drifting wide of the target to the anguish of the home supporters.
With time running out to take a lead into the second leg, the South London side threw everything at their opponents as the rain poured down in the capital. Chris Richards managed to get on the end of a corner at the far post, but his headed effort was steered narrowly over the bar.
Ultimately, Glasner’s side just could not find the quality needed to make the breakthrough, while Larnaca’s impressive resistance and determination sets up a fascinating second leg in a week’s time.
After missing out on the opportunity to secure three successive victories at home in all competitions, the Eagles must now switch their attention back to the Premier League this weekend when they host Leeds United.
Meanwhile, AEK Larnaca are now unbeaten in three games in all competitions and will aim to extend that run on Monday when they travel to Ethnikos Achnas in the Cypriot top tier.
Flashscore Man of the Match: Chris Richards (Crystal Palace)