The Toffees appeared to be heading for their first group stage win of the campaign after goals from Wayne Rooney and Nikola Vlasic had cancelled out Adrian Sardinero's opener, but they were denied by a late Hector Yuste header.
Everton looked sluggish and uninspired throughout, and Koeman is well aware of the task he faces to instill some confidence in his downtrodden side – starting against Burnley in the Premier League on Sunday.
"Sometimes when you are struggling you are too afraid to play football," he told BT Sport. "If it's several players, football is very difficult. We started poor without any confidence, making a lot of mistakes.
"The challenge is to get the team full of confidence. You need to start better - if you start with many mistakes like today it's hard. Look at the first goal; it's shocking. Winning games is good medicine but now it will be the same at the weekend.
"The feeling is like a defeat, not even a draw."
Rooney, whose first-half goal pulled the hosts level, praised Apollon's performance but believes the Toffees deserved all three points.
"We conceded a late goal, but we deserved to win the game," he added.
"They are a good team; there are no easy games in Europe or in the Premier League. We just need that goal to see a game off.
"The goals were sloppy. It's a point but it should be three."