United have endured a shocking April so far, with elimination from the Champions League and two damaging results in the Premier League.
Defeat against Chelsea over Easter was followed by Sunday's draw at Blackburn, leaving United a point behind the Blues having played a game more.
Welsh wizard: Giggs competes for the ball with David Dunn at Ewood Park
But Giggs insists the title race isn't over, saying: 'We will keep fighting to the end and hopefully Arsenal and Chelsea will drop points and we will capitalise.
'It is certainly in Chelsea and Arsenal's hands now. We dropped points at Blackburn which was disappointing.'
Simply legendary: Giggs with Steve Bruce, Mick Hucknall, Sir Alex Ferguson and Peter Schmeichel at an event to honour Eric Cantona on Monday night
United simply must beat rivals Manchester City in this weekend's derby showdown.
'It was always going to be huge at this time of the year, they aregoing for fourth and we are going for the championship and derby daysanyway are massive,' Giggs told Sky.
'There is a bit of extra spice to this game but we have faced themthree times this year and they have all been great games so hopefullythat will be the case again with us coming out on top.'
Giggs added that he is hopeful of facing City despite straining a hamstring at Ewood Park.
Frustration: Sir Alex Ferguson watched his United side drop points at Blackburn
Chelsea can go four points clear of United, with only four games remaining, when they face Bolton at Stamford Bridge on Tuesday night.
United manager Sir Alex Ferguson claimed the match was easy for Chelsea, but Carlo Ancelotti didn't take the bait.
The Chelsea boss said: 'I hope Sir Alex is correct but I don't think so because I have not played an easy game this season.'
Manchester United defender Rio Ferdinand blasts Manchester City star Carlos Tevez - You always took it easy in trainingRooney and Ferdinand in race against time to be fit for Manchester derbyMANCHESTER UNITED FC