Captain Dewi Lake says he always believed Wales could defeat New Zealand and end the 73-year hoodoo against the All Blacks.
Wales never trailed in the 35-28 victory as they produced a magnificent display to beat New Zealand for the first time since 1953.
Wales had lost the previous 34 matches in the fixture and had odds of 20-1 with the bookmakers before this game.
But Lake says the group thought they could win against a New Zealand team ranked second in the world and would have gone top if they had beaten Wales.
"Of course we did," said Lake. "Sometimes we sit in front of the media and say we can beat them and it's probably a passing comment for some media outlets or people at home.
"It's not for us. We work hard, we have tough conversations, not only players, but coaches and staff.
"There is much hard work that goes on for this group to grow and succeed.
"For it to finally come to fruition and see it on the field makes me so proud."
Lake's sentiments were echoed by head coach Tandy, who said he felt emotional after the win.
"You could see what it means for the the players, nation and supporters," said Tandy.
"It's incredible. We've been wanting some positivity and the players delivered that.
"The overriding emotion is pride for the playing group, the staff and I'm just glad for everyone who represents Wales.
"You always have belief. History tells you something different but I believe in the group.
"They are a special group of people and I can't wait to come in every Monday to work with them."
Wales led 14-0 and 21-7 in the first half before the All Blacks levelled the score at half-time.
That is when New Zealand have traditionally gone away to secure victory, as they did 12 months ago in a 52-26 success, but there was no repeat this time.
"I did love it at half-time with the playing group, listening to them talk to each other," said Tandy.
"The way the skipper spoken about around what's coming from the next 40 minutes was outstanding."
Lake added: "I won't tell you exactly what I said because I think that's a privilege that the group that we're in the room should keep.
"But it was more or less a flashback to 12 months ago when we were in a similar position at half-time.
"We were not quite in the lead or drawing, but there or thereabouts and it was just a reminder of that feeling for us."
Wales responded with two more tries before New Zealand brought back the deficit to within seven points.
What followed was a defensive effort rarely seen by Wales in recent years with Gareth Thomas, James Botham, Jac Morgan and Dan Edwards involved in holding up New Zealand over the home line on three occasions, while there were also two vital turnovers from replacement Taine Plumtree.
The home side made 346 tackles, with lock Dafydd Jenkins topping the chart with 38 and flankers Morgan and Botham not far behind.
The work of Tandy and defensive coaching duo Peter Murchie and Dan Lydiate was rewarded with heart and skill.
"The players were brave but also phenomenal and showed great physicality," said Tandy.
"New Zealand threw everything at us but the boys got what they deserved and in big games you have to hang on."
There might have been only 55,152 in the ground, which was the lowest attendance for a Wales and New Zealand fixture at the Principality Stadium, but they roared the home side onto a famous victory.
Lake summed up the events at the final whistle as he was on the sidelines after being replaced.
"It was almost like you were blocked out things, said Lake.
"You heard the noise, but it was like background noise. I think I stopped watching with a minute and 20 seconds left and just waited for the whistle, which I have done before, but this one was different.
"To celebrate with the boys that you work hard with every day, and the coaches that come in and make you better, is an amazing feeling."
Lock Jenkins stated before the game he was asking for Monday off if Wales beat New Zealand, with Tandy's side facing Australia in Cardiff next Saturday.
"We've got to savour moments, because history tells you this doesn't happen very often, and we need to make make sure we enjoy this," said Tandy.
"I'm sure every rugby club out there is going to be celebrating tonight but it's making sure when we come in, maybe Monday afternoon or Tuesday morning, if Daf gets his way, that we're ready to work.
"Because Australia will be a different test."
That can wait as Wales reflect on halting New Zealand's seven decades of dominance over them.
