Wales boss Ryan Giggs has described his team's Euro 2020 qualification as "one of the greatest nights of my life".
Wales had to win in their quest for an automatic Euro 2020 place, and they duly delivered, backing up their achievement in reaching – and then excelling – at Euro 2016.
Giggs followed his predecessor Chris Coleman in guiding Wales to a major championship, and he was understandably elated.
"It is a special, special night," Giggs said.
"The lads have showed great determination and quality and a never-give-up attitude. They deserve all the plaudits. There was no room for error, and the quality and concentration they have shown, they deserve it.
"It is one of the greatest nights of my life. Simple as that.
"I achieved a lot as a player, but it's different as a manager, the pressure you are under and you are helpless as a manager.
"I was never nervous as a player, but as a manager you are. Come game day, it is out of your hands."
Giggs paid tribute to Ramsey, who scored his first Wales goals since September last year – a first-half header followed by a calm close-range finish early in the second period.
"We have missed him," Giggs added. "We have some very good players, but they don't grow on trees – players who make the difference.
"Aaron tonight was the difference. I am really pleased for him."
Giggs was asked if he had won over sceptics, and he said: "I hope so. I'm struggling if it hasn't!
"I asked the players who have been there and done it to climb that mountain again. A lot is made of the younger players, but you can't do it without the older players too.
"Wayne (Hennessey's) double save, Gareth (Bale) putting his body on the line, and it's not easy leaving out Ash (Ashley Williams) who is perhaps the greatest captain Wales have ever had.
"I set out to quality for a major championship, but more than that, to leave Welsh football in a better state than when I took over.
"This is just the beginning. We have seen a lot of young players over the last 18 months, and they can get better – they can definitely get better.
"It probably hasn't sunk in yet. The players can get better with the help of the more experienced lads who aren't over the hill by any stretch of the imagination.
"I didn't think it was a fantastic performance. We showed grit and determination, but our quality on the ball can, and needs to be, better with the quality we possess.
"As a player, you want to play in major championships. My first memory of a major championship was 1982 (World Cup). It's different as a manager.
"This is different. It feels amazing – the group of players I have got and my staff.
"I am a relatively young coach, and I could not have done it without my staff. Together we did it.
"As a player, basically you look after yourself. You are quite selfish, you are. As a manager you have to manage everything, so it's a completely different kettle of fish.
"I didn't think about my playing career, it was all about getting Wales to another championship, as a manager."
Hungary now go into the play-offs for a place at Euro 2020 after seeing their hopes of automatic qualification end.
"We made too many mistakes," Hungary coach Marco Rossi said.
"The first goal was a big mistake. Wales absolutely deserved to win. They showed class.
"The guys tried to fight, but at this level it is not enough. "We are a double-faced team in terms of playing at home and away. It is difficult to explain. We have problems playing away."