The Toffees have made a fine start to 2016-17 under their new boss Koeman, with Monday's 3-0 Premier League win at Sunderland making it 10 points from four games so far.
That left them in third place in the table, but ahead of Saturday's home clash with Middlesbrough, the Dutchman has played down suggestions of Everton challenging for a top-four finish.
Koeman said: "Why after the win on Monday do I need to change from 'fight for European football?'.
"Now we need to fight for the Champions League? I don't know, I think that's not realistic.
"I think it is a big ambition, what I mentioned - that, really, we can fight for Europe.
"We need to continue, and this Saturday is the next one
We need to prepare for that."
Everton finished 11th in each of the last two seasons, during which they were managed by Roberto Martinez.
Asked what he is doing at the club different to how they operated before, Koeman said: "The intensity in training is higher than it was
I believe how you train is how you play.
"Of course, we gave attention to the set-plays
They conceded too many goals from set-plays.
"And (I have given) more responsibility to the strikers and midfield players to help support the defenders.
"Defending starts at the front, not at the back, and it is a whole team performance.
"I think the defensive signings we have made - Ashley Williams, the energy of Idrissa Gueye in the midfield - is a big help for the team.
"Everybody is happy - but (we have to) keep working, and keep the momentum
That is very important at the moment."
Monday's goals came via an 11-minute second-half hat-trick from striker Romelu Lukaku, who had not scored in his previous 13 Everton games in all competitions.
And Koeman said: "It is always a boost, because we know about strikers - they live for scoring.
"Lukaku is always a scoring player, but we need to support the boy, to give him the chances to score.
"I think the offensive side of the team on Monday was great in a few moments in the first half but much better in the second half.
"And one of his qualities is to score the goals
He is one of the best."
Source : PA
Source: PA