The purpose of yom tov isn't only for the yom tov itself. The goal is that it should be good afterwards, too.
Reb Shimshon Pinkus zt'l compared it to a chasan who went home after his chasunah without the kallah! People asked the chasan why he didn't take the kallah home. He replied, "The main thing is that it was a nice chasunah." How foolish! The chasunah is the introduction to married life, not an end to itself.
Similarly, the yomim tovim are meant to bring us to higher places, to an improved avodas Hashem. When the yomim tovim pass, we aren't finished with our service – we need to go further.
A driver stopped at a gas station along the highway to fill up on gas. After his tank was filled, he parked on the side of the gas station and said, “I like it here. It's a good place. There is a good view and plenty of shade. Interesting people come and go... Why leave?” Someone explained to him, “The purpose of a gas station is to get further, not to stay at that spot.”
We just had a Tishrei, we did great mitzvos, and we climbed to greater heights. The purpose isn't to remain there forever. It’s time to move on and draw on the inspiration we acquired for the rest of the year.