United must now beat their city rivals at Old Trafford next Wednesday if they are to defend the Carling Cup at Wembley next month.
Related ArticlesGary Neville gesture under scrutinyMan City 2 Man United 1T?z makes point to NevilleCarling Cup woe for UnitedAge of Manchester City's deference at an endPatrice Evra ridicules Man City ambitionBut Giggs claims that United's cup pedigree underlines their ability to overturn the 2-1 deficit and eliminate their bitter rivals.
He said: 'We made the perfect start because you always want to go 1-0 up in a cup tie away from home.
'But after that, we probably weren't as crisp with our passing and kept playing the ball backwards. We let City back into it, really.
'We felt we were a little unlucky to go into the break at 1-1, but we also knew we could play better.
'But last season we comprehensively beat Derby County in the second leg of the semi so hopefully we can do that again.
'It's going to be tough because City are a good team, but there were enough signs, especially in the last half-hour, to suggest we're good enough to beat them.'
City were thrown a lifeline when referee Mike Dean awarded a 42nd minute penalty - converted by Tevez - following a foul by Rafael on Craig Bellamy that appeared to occur outside the penalty area.
Giggs claims the decision was a key factor, but concedes that United should still have salvaged something from the game.
He said: 'It was a turning point. If we'd have gone in 1-0 up it might have been a different story.
'Sometimes you get decisions and sometimes you don't, so you just have to get on with it.
'We created plenty of chances but we didn't have that stroke of luck or the composure in front of goal. Hopefully we'll have that in the second leg and hopefully we can put the chances away this time.
'After they scored we played well and probably deserved to get that equaliser.'