Martin O'Neill wants his Republic of Ireland team to create more magical moments when they play at the Euro 2016 finals in France next summer.
The Irish sealed their place by beating Bosnia-Herzegovina 2-0 in Dublin on Monday, clinching a 3-1 aggregate win.
"This is a special night which cannot be taken away from us," said O'Neill.
"We will have a massive contingent of fans going to France and I would like to emulate the days of Jack Charlton and Mick McCarthy."
- More reaction to the Republic of Ireland's play-off success
- Listen to both goals and the moment the Republic qualified
- 'Roy Keane actually cracked a smile' - podcast
'We won't just be making up the numbers'
Northern Irishman O'Neill, 63, will enjoy his first experience of tournament football as a manager when he leads the team out in France, having progressed from a difficult group including world champions Germany, Poland and Scotland.
"I could not be more proud. The players have been superb right from the start when Aiden McGeady scored that late winner in the first qualifier in Georgia.
"We might be short on a few things, but courage and a determination to fight to the end have been in abundance."
Roy Keane - whose appointment as assistant manager O'Neill described as "as good a decision as I have made for a long time" - told RTE: "We do not want to go there just to make up the numbers.
"We will go there to do the country proud and put on a good performance. Doing your best, that is all you can ask."
It will be Keane's first experience of a major tournament since walking out of the squad during the World Cup in Japan and South Korea in 2002 following a dispute with McCarthy.
|Republic of Ireland||Ukraine or Slovenia||Denmark or Sweden|
'These are special moments'
Double goalscorer Jon Walters said he was determined to savour the play-off success.
"To qualify the way we did is unbelievable," said the Stoke forward.
"You have to take it in because these things do not come around often in your career. These are special moments and we are delighted."
Walters, back in the team after suspension, got his first goal with a disputed penalty midway through the first half and made it 2-0 on 70 minutes.
"The whole team were heroes - everyone was incredible," he added. "We had to work hard, but we got there."
'This is what you dream about'
Robbie Brady, whose free-kick led to the second goal, said the victory was the highlight of his career.
"This is the type of thing you grow up dreaming about," said the Norwich City winger.
"We did what was required and now we are off to France.
"We never seem to do things the easy way, but we stuck together during the campaign and got the incredible results we needed."