When the squad was confirmed earlier this month, Senegal striker Niasse had not made an Everton first-team appearance since May 2016, with him having spent time banished to the U23s and then on loan at Hull.
But he returned in some style last week, coming off the bench to score once in the 3-0 Carabao Cup win over Sunderland and twice in Saturday’s 2-1 Premier League victory against Bournemouth.
Asked ahead of tonight’s Europa League home clash with Cypriot side Apollon Limassol if it was frustrating not being able to call upon Niasse, Koeman said: “No, because we had to make that decision. I think a long time ago.
“At that time his situation was not the situation of now. In life you don’t get a second chance, and you have to decide.”
The Dutchman added: “I believe we need to improve our attacking, but I am not worried because I believe in the qualities of our strikers.”
Everton will also be without midfielder James McCarthy, who has been sidelined by a knee problem and is yet to play this season.
On Tuesday, he was named in the Republic of Ireland’s provisional squad for World Cup qualifiers against Moldova on October 6 and Wales three days later.
Koeman had a war of words with Republic boss Martin O’Neill last term over McCarthy’s use by the national team after suffering injury.
The Everton manager was asked yesterday how he regarded McCarthy’s condition and the call-up, and said: “Every nation is free to call the players. They need to see the player, and then if it’s possible.
“I heard from the doctor he can be part of the team for training this Friday. But his last game was in July. I think that is the answer for you.”
Wayne Rooney, left with a cut above his left eye and a bloodied face on Saturday having been caught by Simon Francis’ arm, is fit to feature.
But centre-backs Michael Keane (foot) and Phil Jagielka (hamstring) remain unavailable, and are also doubts for Sunday’s league match against Burnley.
Everton head into what is their second Europa League Group E game having been woeful in their opener, the 3-0 away loss to Atalanta.
That was part of a six-game winless run and four successive defeats, halted by the Sunderland victory.
Koeman added: “The two wins were important, but this is a different competition.
“We need to react, because what we saw in Italy was not the Everton we like. We have to show that revenge feeling tomorrow.
“You play three games at home in the group stage and you need to win those.”