Neville has been involved in much of the fallout from their 2-1 defeat at Eastlands last Tuesday as his spat with former team-mate Carlos Tevez, City's two-goal hero, escalated almost every day.
And although the England international is focused on the midweek second leg at Old Trafford he acknowledges the prospect of a trip to the Emirates Stadium has huge significance in what he deemed a three-horse race for the Premier League title.
Going top: Wayne Rooney scores his third goal in Saturday's win over Hull
'The fact that we played a strong team in the Carling Cup against City shows how important the match was,' said Neville.
'We want to get a consistent run of performances now. At the moment we have to play a strong team to try to win every match and hopefully win trophies.
'We are getting to the business end of the season and we want to make sure we are competing in finals and competing for the championship.
City slicker: Carlos Tevez scored twice last week to put pressure on United in the Carling Cup semi-finals
'Nothing is won and lost in January, but at the moment Arsenal,ourselves and Chelsea are looking like the teams most likely to mount achampionship challenge.
Case for the defence: Neville knows United face a tough week
'It's not too late for teams behind us toput a run together. But there is a gap (10 points) now between the topthree and the rest, and it can be very difficult to close such gaps.'
On the looming trip to Arsenal next Sunday, Neville added: 'It's always difficult to go to the Emirates and Arsenal are a very good side in good form, so it's a big week for us and one for us to look forward to.'
Despite Saturday's 4-0 thrashing of Hull, with Wayne Rooney scoring all four goals, the 34-year-old is still smarting from the defeat by their city rivals, during which Tevez and Neville exchanged gestures and later Tevez called his former team-mate 'an idiot' and 'a boot-licker'.
'Our attacking play probably deserved more than one goal but the beauty of a two-legged tie is we live to fight another day,' Neville wrote in the Times of Malta.
'We conceded two goals, which was disappointing, but the great thing about this tie is we've got another opportunity to put it right on Wednesday. It's all to play for.'
Police on red alert amid fears over Manchester derby cup clashMARTIN SAMUEL: Once a red always a red? It's not a sure thing for Wayne RooneyMANCHESTER UNITED FC