The Black Caps won the five-match ODI series 4-0 and the two-Test series 1-0, the latter thanks to a superb triple-ton by McCullum, which was the first by a New Zealand batsman.
"Yesterday (Tuesday) stopped a nation to a degree," said Hesson, talking about the final day of the second Test versus India here.
"A lot of people took a great deal of satisfaction out of it. As a New Zealander, not only as coach, it was a pretty special moment. A lot of people were touched by it and gained lot satisfaction from it and quite rightly so," he added.
McCullum scored 302 runs in the second innings of the Test at Basin Reserve, overtaking Martin Crowe's highest Test score for a New Zealand batsman (299 scored against Sri Lanka at the same ground, way back in 1991).
"We saw that real emotion come out when Brendon got his 300. We all sat on the same seats for a couple of days, ate the same food and tried do as little as we could. When he got to 300 you saw true emotion come out and we were all delighted for him," he said.
"He (McCullum) was pretty sore after day three and four but I guess it's a good sore. Once he got 300, he looked a lot fresher than an hour before. It was just a special time to be part of," he added.
New Zealand were bowled out for 192 in their first innings and India scored 438 in reply, taking a 246-run lead.
The hosts were then reduced to 94/5 at one stage but overturned that to take a 434-run lead and deny the visitors a chance to level the series, after the first Test at Auckland ended in a 40-run victory for the Black Caps.
"The fightback defined the way we want to play our cricket. Sure, we don't want be 200 behind but we lost pretty much every important toss over the whole summer and got ourselves in some tricky positions and kept fighting out of it. We were in the trickiest position of all two and half days ago. The way Brendon and BJ (Watling) played was exceptional.
"Then, the way Jimmy (Neesham) came out and took the pressure off Brendon from a scoring point of view, he just went about his work. He'd been sitting there for nine hours," Hesson said.
"He went up against the third new ball and we were still only 200 ahead, still under the pump, to play with the freedom and the skill he did was exceptional. You find out about people when they are really under the pump," added the proud coach.
Victory in both ODIs and Tests against India rounded up a great summer for the Black Caps, after they beat the West Indies in Tests and T20s earlier.
They now have to play South Africa and Pakistan before heading into the 2015 World Cup which they will host jointly with Australia.
"We've performed in all three forms and thats something we haven't always been able to do, and all the guys thoroughly enjoyed it. We have more ODIs in the year ahead, so a lot of cricket to be played before the World Cup," Hesson signed off.