Everton fell two goals behind by half time thanks to Harry Kane's fortunate opener where a cross-cum-shot from wide on the right deceived Jordan Pickford and Christian Eriksen's predatory strike following poor defending by the home side.
Kane killed the match less than a minute into the second half when he turned in Ben Davies's cross from an unmarked position.
“In the second half you could see we were far away from Tottenham, but in the first half an hour we were much closer," Koeman said following his team's second successive defeat.
“We knew they could change systems and play three at the back but, okay, we were surprised a little bit by the way they played in midfield.
“It made it difficult for us. We changed some players to try and help us in the second half but we conceded the third goal straight away.
“I've said before I think, along with Manchester City, Spurs are the best footballing side (in the Premier League). The difference is they have had the same group of players for a long time now.
“If you think we are trying to join them in that [top six] pack, it will be really difficult.”
Koeman was critical of his outfit's lack of fight in the game following Kane's opener but admitted that the timing of the third goal destroyed what little confidence may have been left.
He also cautioned about keeping expectations in check following Everton's big-spending summer may also be a factor, repeating his recent mantra that it will be hard for the Blues to crack the top six this season.
"I do not ask for yellow or red cards, but in several situations we were too nice," Koeman continued. "I saw some Tottenham players [that were] really clever in the battles. We were too nice, too weak in the second-half.
"But I think that also has to do with confidence. The third goal straight after half-time killed the confidence in the team.
"I know how it works in football. If you sign some players, [people tend to stop] being realistic," he said.
"Everybody is talking about Everton and the top six. But if you know the qualities, and the individual qualities of the players in the top six, it is a challenge.
"It is our ambition, but we need to realise it is difficult.
"We will learn from the mistakes today and we have enough games coming up to have a good reaction."