Roberto Mancini has warned his Manchester City players they face a fight right until the end of the season from neighbours Manchester United for the Premier League title. United briefly replaced big-spending City at the top of the table after a 2-0 win over Queens Park Rangers on Sunday before Mancini\'s side returned to the summit following their 1-0 defeat of Arsenal later in the day. David Silva\'s winner -- City\'s 50th Premier League goal of the season -- restored his side\'s two-point advantage at the top and left Arsenal manager Arsene Wenger declaring his team\'s title chances had all but vanished. But ahead of a busy festive programme, Mancini has told his men to prepare for a battle to the end of the season with reigning English champions United. \"We can\'t think that we can win the title without a fight from United,\" said Mancini. \"It\'s impossible. \"We want to stay top for a long time -- not only for Christmas,\" City\'s Italian manager added. City, who entertain Stoke on Wednesday, produced the perfect response against Arsenal after their unbeaten league start was ended by Chelsea last Monday. Pablo Zabaleta hit the woodwork but Silva\'s fifth league goal ensured it was business as usual at Eastlands. \"We are delighted because after losing to Chelsea it was really important to beat Arsenal,\" said Mancini. \"We deserved to win the game. We didn\'t deserve to lose to Chelsea but that is football.\" Reflecting on the win over the Gunners, Mancini said: \"It was a great game, not for the managers, but for the supporters. We had a fantastic performance as Arsenal are playing very well at the moment. \"When you play against Arsenal they have players like Gervinho, (Theo) Walcott and (Robin) van Persie who can score at any moment. \"For our character this was a big test and we showed we are a strong team.\" Arsenal were frustrated by a brilliant display from City goalkeeper Joe Hart. The England international produced a string of excellent saves to frustrate van Persie, Thomas Vermaelen and Walcott. Defeat left Arsenal 12 points adrift of City and Wenger conceded it would be tough for the Gunners to win the title from such a long way behind. \"It will be difficult to close the gap on City now, but we will try,\" said Wenger, who lost defender Johan Djourou to a groin injury which could sideline the player for three weeks. \"This was a game we couldn\'t afford to lose. It\'s difficult to take but we will continue to fight. \"Losing Johan didn\'t help. We are short on the flanks and every injury at the back is detrimental to our performance,\" the Frenchman added. \"(Laurent) Koscielny, Djourou and Vermaelen did remarkably well but they are centre-backs. \"But it is a good basis to build from. Both teams played played positively and that\'s why the game was interesting. It was also intense physically.\"