Gaffers View: WHU home 4-3 agg
But it could have been oh so different and it looked to be all over when Carlton Cole found the net with a long range effort that made the score 3-1 on aggregate.
But after a bit of encouragement from the boss at half time Blues fought back to take the game into extra time before dispatching the Hammers out of the competition with a goal from life-long City fan Craig Gardner.
Serbian striker Nikola Zigic also helped to turn the game on its head when he was introduced after the break.
McLeish said: 'It was a really exciting moment for me when the final whistle went in realising what myself, my staff, the players and everyone has achieved.
'It was a magnificent second half and to walk a team out at Wembley will be one of the proudest moments of my career.
'The first half was a huff and puff job from us and they looked quite comfortable and Cole scored an amazing goal.
'I thought at half-time 'we are out of the cup, we have to make changes, change the tactics and approach.'
'Nikola Zigic had his best game for the club and was much more aggressive and he realises what it takes to be a success in England and that is the best I've seen him.
'He was almost unplayable. He was verging on that.'
Now it`s Arsenal in the final and McLeish knows that it is not going to be easy.
He added: 'They will be hot favourites and have been for a couple of rounds now but you never know.
'It is XI v XI. We will try and get the tactics and strategy right and try and cause a major upset.
'We have to embrace what comes along and try and deal with it.'
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