Chris Coleman has told his players to prove they are the best Wales team since 1958 by qualifying for Euro 2016.
Gareth Bale scored twice as Coleman's side went top of Group B with a 3-0 win in Israel on Saturday.
Wales have not reached the finals of a major tournament since playing at the World Cup in Sweden 57 years ago.
"We've got the chance to prove we are the best Welsh team since the one that qualified for the 1958 World Cup," Coleman said.
Wales reached the quarter-finals of the 1976 European Championship, in the days when only four teams played in the finals, and narrowly failed to qualify for the 1994 World Cup and Euro 2004.
In November 1993, Terry Yorath's Wales team would have made the World Cup finals by beating Romania in their final qualifier, but lost 2-1 at Cardiff Arms Park.
Under Mark Hughes, they missed out on a place at Euro 2004 after losing 1-0 to Russia in a two-legged play-off in November 2003.
Coleman said: "We nearly did it in 1994 and 2004 and now we have the opportunity to go a step further.
"People say it's a golden generation but we need to earn it. We're doing it but we've not done it yet.
"We want the chance to prove since 1958 this team is as good as anything that's gone before."
'I don't need to answer the critics'
Two Bale goals secured victory for Wales after Aaron Ramsey had scored in first-half stoppage time.
Bale has been criticised heavily in the Spanish media as his club side Real Madrid have faltered in La Liga, slipping behind Barcelona in the title race.
"I don't need to answer the critics," Bale told BBC Wales Sport. "I know and everybody around me knows what I can do.
"There are ups and downs in football, but you have to take it with a pinch of salt. All you can do is respond with performances on the pitch."
Arsenal midfielder Ramsey limped off late on with a groin problem, but said: "I feel OK."
'20 points the target'
|Wales' remaining Euro 2016 qualifiers|
|12 June: Belgium (h)||3 Sep: Cyprus (a)||10 Oct: Bosnia (a)|
|6 Sep: Israel (h)||13 Oct: Andorra (h)|
Victory in Israel has given Wales 11 points from their opening five qualification matches, and Coleman feels a further nine points from their remaining five games will be enough to take them to the Euro 2016 finals in France.
"You've got to be really unlucky if you get to 20 and you don't get in the top two," Coleman said.
"We've done some good work and we're on the right road but there's some distance left."
Manics love Gareth
The Manic Street Preachers were among those to show their appreciation of Wales' victory - and for Bale.
Posting on their Twitter feed, the Welsh rock band wrote: "Dear Mr Bale. Whatever they think of you in Madrid, WALES LOVES YOU xxx Brilliant performance from everyone."
Bale himself tweeted: "What a performance from the lads!"
Leicester and Wales midfielder Andy King added: "The lads have been different class! A deserved 3 points, Congrats to the skipper Ashley Williams on his 50th cap also."
Match of the Day host Gary Lineker, who played in Spain for Barcelona, gave Bale some words of encouragement: "Every player has the odd dip in form, it's how you respond that's important. Mr Bale appears to be responding well. Take note Merengues [Real Madrid]!"