The Scot believes Harry Redknapp's side are genuine title contenders, but remembers a time not so long ago when the two clubs were battling it out for European qualification.
But while Tottenham have built on their Champions League debut last season and can move within three points of Premier League leaders Manchester City with a win on Wednesday at White Hart Lane, Everton are mid-table and 18 points behind their hosts.
And Moyes knows counterpart Harry Redknapp has benefited from having access to one thing he has not - money.
"It is a little bit sad they are starting to pull away from us a little bit more than I would like," Moyes said.
"I think it was only three or four years ago us and Tottenham were competing neck-and-neck for European places.
"It is frustrating because all managers will tell you when you are close and competing with teams you never like to see them go away from you, but we are looking at them going away from us at this present time.
"They have continued to kick on and over the years they have got in some really good players. Rafael Van der Vaart is one and Scott Parker another recently.
"Tottenham, arguably, might be the biggest spenders in the Premier League - they have always supported whoever the manager has been.
"Football will always come back around sometime and some day hopefully they will be looking at the back of us.
"At the moment it unfortunately looks as if you need a bit of finance to get it back, but it would be nice to think we could do it the way we have done it.
"We will work really hard and try to bring in players, produce our own players here, work with them, develop them and try to make them better.
"That is how we do it at Everton, we don't do it any other way."
Moyes can only look on enviously at the resources which have been made available to Redknapp, who signed Parker from West Ham for £5million and brought in Manchester City striker Emmanuel Adebayor on loan.
Moyes brought in Royston Drenthe and the unknown Denis Stracqualursi on loan and added free agent Marcus Hahnemann as goalkeeping cover.
However, he concedes that money is not solely responsible for Tottenham's success.
"They have a really good team and are title contenders. I think Harry mentioned it last season that he thought he was quite close," he added.
"I agreed with him because I thought we had a good chance last year of making the Champions League.
"Harry has come in and done a brilliant job with them and that is why, more than likely, it might see him become England manager.
"I think it would be great for England and deservedly so because he has a really exciting team, I think a team I would probably pay to go to watch,
"What they are doing and the way they are playing is terrific."
Wednesday's match was originally scheduled for the opening day of the season but had to be postponed because of the riots in London.
Moyes would have much preferred to be playing Spurs in August instead of now, but having lost just once in their last five visits, the Everton manager remains positive.
"By Harry's own recognition they were not in the best shape in the first few weeks of the season," Moyes said. "But it didn't happen so we have got the game now.
"Over the years the games have always been tight. Harry knows when he plays Everton his team have to play well to get a result and we will have to play really well because they are a very good side."