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The Crusaders head coach was among the finalists for the All Blacks job after the departure of Steve Hansen following the 2019 Rugby World Cup campaign, but was overlooked in favour of Hansen's longtime assistant Ian Foster.
"There's always a natural process as a human, there's a natural disappointment because I've put everything in to it," Robertson said of his unsuccessful campaign for the All Blacks role.
"They think they have the best man for the job and, look, through the process I did everything I possibly could; they got who I was and how I would have loved to have led the All Blacks and they were clear with my vision and how we were going to do it, but it wasn't to be.
"It's been a good four months, hasn't it? It feels like it's been an election in its own way. I prepared well, everyone understands what I've done with my record…I had a great two and a half hours in front of the board and it went another way.
"I flicked a text [to Foster] to say congratulations to him. It's been a big few months and obviously it's nothing personal, he's in a position like me and wants to do the best for himself and the country."
The 45-year-old Robertson has amassed an impressive record as head coach, with a winning percentage above 80% during his time at the helm of Canterbury and the Crusaders. Since taking over at the Crusaders for the 2017 season, the club has won 48 times and lost just five matches.
After the announcement of Foster's appointment was made on Wednesday, many commented that Robertson would be lost to New Zealand Rugby as another national system would pounce on the opportunity to lure him away. However, with two years remaining on his contract, Robertson brushed those suggestions aside.
"I'm coaching the team I love, where I've had a lot of great moments as a player and now as a coach, I've got a lot of special bonds and a chance to do something pretty special," he said.