It was the visitors that took the lead originally after a stray Ashley Williams pass resulted in a crossed ball being turned in under Jordan Pickford by Sardinero Corpa in the 12th minute.
Everton responded 10 minutes later however, when another poor defensive pass, this time from Hector Yuste, evaded his teammate in goal, falling perfectly for the eager Wayne Rooney, who was left with a simple tap-in.
The home side did in-fact take the lead through Nikola Vlasic on the 66th minute mark after the Summer signing replaced Idrissa Gueye at half time. However, it wasn't enough to secure the three points as a free-kick in the 88th minute was headed in for Limassol by Hector Yuste.
Coming away from the game, Ronald Koeman has a lot to take into this weekend's fixture against Burnley - most of all the fact that he is under immense pressure from fans and the board to improve form.
Give youth a chance
It was clear when 19-year-old Vlasic and later 20 year-old Dominic Calvert-Lewin were introduced that the youngsters within Everton's squad are the ones looking to make a difference.
The determination and willingness shown by the Croatian upon introduction was breath of fresh air among fans. The direct running was completely absent in the first half, as the team involved three holding midfielders and three number tens.
Vlasic added width - something that Everton are in desperate need of, which brought an alternate crossing option when attacking, also allowing Leighton Baines to overlap as is his signature move, to create another dimension of play.
Not only did Vlasic eventually put Everton ahead with his first Everton goal since signing for £10 million, but he almost assisted in giving Everton a third, as it was his cross that found Calvert-Lewin in the middle, only for his header to be parried away by the opposition keeper.
The young Englishman was just as effective in attacking however, as he displayed his attacking intelligence through constant movement off the ball and fantastic vision when in possession of it.
Experience isn't always key
As demonstrated particularly well by Williams, it is clear to see that experience isn't always key, as sometimes it just doesn't add anything to the team.
Since his arrival at Goodison Park, Williams has had a very awkward time - being sent off once, committing an impressive 46 fouls thus far, and this season having no clean sheets.
It is unfortunate, however, that Everton have sustained injuries to club captain Phil Jagielka and Michael Keane who have shown a better understanding as a partnership, leaving Mason Holgate (typically a right back) to deputise in their absence.
It's a similar story for Rooney. Despite being Everton's top scorer in all competitions with three goals, Wayne Rooney has offered very little in the starting line-up. As a striker, he has been outshone by Calvert-Lewin, and as a number 10, Gylfi Sigurdsson has bettered him.
It appears as if Koeman is afraid to drop such experienced and crucial players, which is within reason, but he must understand that there is a point in which it must change, and that appears to be now.
A change in formation is needed
Thus far, Everton have been regimented in a trademark 4-2-3-1 or a 4-3-3, but what once worked wonders for the Toffees is now their downfall.
The main issue again, is width. Playing a formation that involves two wingers, and playing two number tens instead is a huge fault of Koeman's, especially when there are wingers or players competent of taking on such a role such as Vlasic and Sandro on the bench.
Playing two anchoring midfielders in a double pivot has worked very well for Everton over the years, but it seems to be restricting attacking freedom when they need it most.
Idrissa Gueye and Morgan Scheiderlin are both adept in regaining possession and passing from midfield due to their seemingly unlimited stamina. However, against teams such as Apollon Limassol where goals shouldn't be overly hard to score, the inclusion of both seems unnecessary.
Rather, it'd make sense for Everton to set up in a 3-4-2-1, with Baines and Jonjoe Kenny as wing-backs providing width, then leaving the Everton boss with a choice of whether to play number tens such as Rooney, Sigurdsson or Davy Klaassen in behind a striker or have wide forward such as Vlasic or Sandro.