Everton secured a 1-1 home draw with Tottenham Hotspur in their season opener before winning their next four league games, sparking speculation they might emulate last season's unlikely champions Leicester City.
Koeman, however, dismissed talk of the title as premature and unrealistic.
"It's a good start but we know it is very early and there is a long way to go," the manager told reporters ahead of his team's League Cup match against Norwich City later on Tuesday.
"I don't think we can do a Leicester. I am realistic. If I tell you we will fight for the title I think most people will tell you that man is crazy. Even when I mention that it sounds crazy.
"Why would we change our ambition and aspiration after 13 points from five games? The big teams have much more qualities and unless it is like it was last season it will be impossible."
Koeman, whose stated aim is to get his team into next season's Europa League, said Everton needed to get better to hit even that target.
"We need to improve and we can improve if we want to fight for Europe," he added.
Striker Romelu Lukaku is out of the Cup game with an injured toe with new signing Enner Valencia set to start in his place.
Midfielder Darron Gibson will not return to action for another three weeks after undergoing surgery to fix a groin complaint.
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
