United maintained their 100 per cent start in the Premier League under Jose Mourinho on Saturday courtesy of teenage substitute Marcus Rashford's stoppage-time goal at Hull, which clinched them a 1-0 win.
Left-back Shaw has made an impressive start to life back in the spotlight for United after sitting out last season with a broken leg and is expected to be included when Sam Allardyce names his first England squad later on Sunday for next weekend's World Cup qualifier in Slovakia.
But the 21-year-old is also looking beyond that as a crucial showdown with their title-rival neighbours beckons.
"We want to win every game and this game is over now," Shaw told United's official website at the KCOM Stadium.
"We've got to focus on the international break but obviously we have the big game against Manchester City when we come back.
"We know matches like that can help us win championships."
Shaw said he had never felt so high on the pitch after Rashford's winner in the second minute of time added on had made it three wins from three in the Premier League.
"I think, emotion-wise, that was the best I've felt ever on a pitch," Shaw added
"I'm just so happy that we could get the three points, not just for us but for the fans
They were unbelievable
"It was an unreal feeling and even a few of the lads in there (the dressing room) said it was like taking them back to the old days when they sometimes used to get those smash-and-grab wins
I loved it and hopefully there's more to come."
Hull caretaker boss Mike Phelan is expecting a frantic few days before the transfer window shuts on Wednesday
Five long-term injuries have left him with a threadbare squad - he had 13 senior players to face United - while the club's pending takeover has meant no new arrivals since the end of last season.
"It's going to be touch and go," Phelan said
"It's going to go until midnight on Wednesday or midday in some countries.
"Hopefully we can settle all those issues we've got in front of us
We need football players.
"I don't think we can be particular anymore
We're in the market for players.
"We still have that 13-man squad
Yes, we have four or five injuries, some of them are a bit more long-term than others, but we need to add.
"We need a squad, certainly to get you through to January anyway.
"We've made a great start and we need to back that up now with some new players, just to give us a helping hand to take us on and further."
Cardiff have accepted an offer from Hull for goalkeeper David Marshall, who will now discuss personal terms, and it is understood the Tigers have met Tottenham's valuation of midfielder Ryan Mason, while further recruits in all areas need strengthening.
Phelan confirmed Robert Snodgrass will have his injury assessed by Scotland's medical staff after the winger was forced off against United due to a tight calf.
Source : PA
Source: PA