Leigh is relieved to see his side in Monday's draw.
He said: '˜I am just happy to be in the hat because after the first half I was relieved to still be in the game.
'˜Our opponents were the best we have played this season.
'˜They really stopped us playing our football with their pressing and work rate.
'˜The goal we got just before half-time was crucial and lifted everyone.
'˜In the second half we dug in and showed great character to get in front.
'˜Then in the final 15 minutes they threw everything at us and bombarded our goal.
'˜But we dealt with it and hung on for the win.'
The home side suffered a set-back early on when Ashton Leigh missed from the penalty spot.
Bournemouth capitalised on this to score twice but Shane Cornish reduced the arrears from the spot two minutes before the break.
Callum Dart levelled soon after half-time and Jason Parish netted the winner.
Two first half goals were enough to sendÂ HorndeanÂ out in a 2-0 defeat at Chertsey Town.
Michael Birmingham felt his side gave a good account of themselves against powerful opponents.
The Deans boss said: '˜Sometimes you have to hold your hand up and say you were beaten by a better side.
'˜I wouldn't be surprised if they went all the way to the final.
'˜We missed a good chance in the opening five minutes which could have made a difference.
'˜Then we had a 10-minute spell when we shot ourselves in the foot and conceded two goals.
'˜In the second half we were better but huffed and puffed without getting anywhere.
AFC PortchesterÂ enjoyed a 2-0 win against Bemerton Heath Harlequins in the Wessex League premier divisionÂ at the Crest Finance Stadium.
Dan Simmonds and Joel Jackson grabbed the goals to get the Royals back winning again.
Fareham TownÂ slumped to a 5-2 defeat at Shaftesbury.
In division oneÂ United Services PortsmouthÂ beat New Milton Town 4-0 at the Victory Stadium.
Lewis Beale scored twice, while Mig Dark and Tom Jeffes also netted.Â
Petersfield TownÂ forced a 0-0 draw at Whitchurch United.