The English team got close to perfect in their sweep of Pakistan.
England became the first team to leave Pakistan with a series victory when they won the third Test by eight runs.
"It's been an amazing four weeks, it's been incredibly satisfying," he said.
We will leave this tour knowing that we achieved something very special.
Prior to this tour, England had not beaten Pakistan in a Test outside of the UK for 22 years and had only ever won two matches against the same opposition.
In Pakistan, England recorded only their fourth away clean sweep against any team in history.
The first Test in Pakistan was won by England on a flat pitch at the end of the fifth day.
A tense finish in the second Test resulted in England prevailing by 26 runs, and the emphatic win in the finale came after the toss was lost.
The first day of the first Test was at risk of being delayed due to an illness that has lingered around the squad.
The New Zealander said that every ground has challenged them. Some of the challenges we faced were tactical, technically and mentally.
The guys were sick during the tour. We got close to perfect because they have been able to play the style of cricket that we have on those three grounds.
The tour has seen the emergence of a batter who scored hundreds in each of the Tests.
Bairstow will return to the team as soon as he is fit after he broke his leg.
The leg-spinner Rehan Ahmed was England's youngest man to play international cricket at the age of 18.
The Leicestershire man is entered in the Indian premier league auction on Friday.
"Now is the time for us to look after him," said McCullum. He'll be encouraged to play a lot of franchise cricket and play with different players under different coaches and in different conditions.
If he got picked up, it would be great. It would be great if he could rub shoulders with other players and pick up some experiences. There are other 18-year-olds who are going to get those chances. He's a full member of the international cricket team.
Since the beginning of the home summer, England have won nine of the 10 Tests they have played.
"We all know what we've done is special," he said. It will be something to look back on, and be very proud of.
It's a good time to play for England. If things don't go well, the real test will be if we are able to win. I hope we don't go that way.
There are two Tests in New Zealand in February. They play a one-off match against Ireland in June in order to get ready for the return of the urn.
"I don't want to look too far in the future," he said. There are a few things in the back of my head that I'm interested in.
We will continue to grow as a team and play cricket with a smile on our face and win as much as we can.
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