First-choice at the start of the recently-ended season, Annan lost his starting spot for good to Ghana U23 goalkeeper Kwame Baah after taking time off to tie the knot with his girlfriend.
The situation led to speculation about bad blood between the two goalkeepers while other reports say Annan is considering a move away in his search for regular action.
"Felix used to be our first-choice goalie before his wedding ceremony but Kwame Baah grabbed the opportunity and did very well without conceding in most matches so how can you drop him?" Appiah said on Kweku Osei TV.
"The supporters would kill us if Annan underperforms if given the nod. There's no personal hatred for him but [we are just] following the rules of the game.
"Hard work will be the secret of him regaining his position devoid of any envies."
Annan’s recent peripheral role at club level has seen him lose his place in Ghana’s national team squad.
He was appointed Kotoko captain in August last year following the departure of defender Amos Frimpong.
At the time, current Ghana coach CK Akonnor was leading the Porcupine Warriors.
“All my years at Kotoko and my playing career, I have been fighting for positions,” Annan told Kotoko Express App on the situation in April.
So far as I'm in the club, I'm going to fight and give my best every minute I step onto that field.
“For me, [being out of favour] is not a problem at all.
"It's all about keeping on with my training and I will keep on fighting until I am no more in the club.”
Annan joined Kotoko from Feyenoord Academy in 2014.
"It is technical decision-taking from all the coaches in the team a night before a game,” Kotoko coach Konadu explained to Kotoko Express App.
“We gave Kwame Baah a chance after Felix Annan had excused himself for his wedding and he didn’t disgrace himself and it was okay with us.”
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