Phil Foden sees Champions League glory as the main prize as Manchester City continue to fight on four fronts.
The Premier League leaders remain in the hunt for a historic quadruple and meet Chelsea in the final of the Carabao Cup final at Wembley next Sunday.
Before that City, who reached the quarter-finals of the FA Cup by beating Newport 4-1 on Saturday, return to Champions League action with a last-16 tie at Schalke on Wednesday.
Foden scored twice at Rodney Parade – the first double of his senior career – and the 18-year-old Stockport-born midfielder impressed throughout, with TV presenter and former England striker Gary Lineker describing him as "a great talent".
"It's been a long while, it feels like it's been gone for ages," Foden said of the Champions League's two-month break.
"I'm looking forward to getting back to the Champions League.
"That's the main one, so we'll see if we can get a result in that.
"We are still in all competitions and we want to keep fighting for every one – and hopefully we can win them all.
"We're going to try. We know it's very difficult, don't get me wrong. But I can't see why we can't do it."
City had to overcome resilient League Two opponents 82 places below them in the English pyramid, and a bobbly pitch that was bare in places to make the last eight of the FA Cup.
Newport had a gilt-edged chance to open the scoring through Tyreeq Bakinson and became only the fifth team this season to prevent Pep Guardiola's team from scoring in the first half.
But Leroy Sane struck six minutes after the interval, and Foden scored either side of Padraig Amond's chip before Riyad Mahrez added a fourth in stoppage-time.
"We are Premier League footballers so we can handle any pitch," Foden said.
"It was always going to be a difficult game on the pitch, but in the end we showed our quality.
"It was tight but we just had to keep doing what we were doing, and that was the message at half-time.
"We knew they would tire and they did in the end."
Newport return to the fourth tier having made over £1million from reaching the fifth round for the first time in 70 years.
Wins over Leicester and Middlesbrough furthered a giant-killing reputation established last season when Leeds were beaten at Rodney Parade and Tottenham were held before a Wembley replay was lost 2-0.
Several County players have appeared as if they could perform regularly at a higher level, none more so than Irish striker Amond whose late chip gave him a goal in every round.
"I'm disappointed that we've lost the game and we're out of the cup, but in years to come that's going to be something I'm very proud of," Amond said.
"Also the fact that I've scored against the best team in Europe.
"Pep came over after the game and congratulated me that I'd scored, and when you hear that from someone like him it means a lot.
"It's been a great run, you have kids wanting to play for Newport County and maybe before that they wanted to play for Cardiff, Bristol, Swansea. The club can be very proud to inspire a new generation."