Koeman believes that the opening goal was a pivotal moment in the match and admitted that his side must improve significantly if they are to push for a top-six finish this season.
"Maybe after Lionel Messi and Cristiano Ronaldo and Alexis Sanchez, and maybe one or two more, [Kane] is one of the best. Of course the first goal is a lucky one. I don't think he was supposed to shoot the ball in the goal - I think it was a cross. But in his football he is really clever. He is using his body at the right time, his movements, his finishing. He is a top striker," Koeman told reporters.
"I think until we went 1-0 down, we did well. Then going 1-0 down broke our confidence a little bit. We had problems with the diamond in the Tottenham midfield. They scored the second goal before half-time and at half time we tried to pick up the team. We changed, making two substitutions, and changed a little bit the positions in midfield, to have a better control. But if you go out of the dressing room and start how we did in second half... That was poor.
"There was a misunderstanding between Michael Keane and Jordan Pickford, and after that, the next situation was that we were 3-0 down. Then I understand how difficult football can be - one team is full of confidence at that time, we were without any confidence. Then you see the difference.
"If you look at the second half, we are really far away [from top-six standard]. If you look at the first 30 minutes, it is different. But the difference between Everton and Tottenham is that they have worked a long time together now with the same players and it is not realistic to expect that Everton already is at that level. If you think we need to be at that level, then it will be really difficult."
The defeat leaves Everton 15th in the Premier League table with four points from their opening four games.