Scott Jones netted a first-half brace to fire the Hawks into the fourth round of the Hampshire Senior Cup.
But Shaun Gale was left counting the cost of the 2-0 triumph at Blackfield & Langley last night.
The Hawks boss was fuming after Chris Holland was shown a red card in the second period.
The centre-back will now miss the club’s crucial Christmas period.
Gale said: ‘I am sick to death of this competition – all it does is throw up problems.
‘We have had a player sent off who will now miss two games over the Christmas period.
‘And neither side could understand why the players got sent off.
‘It is a man’s game but all it seems to be about is the officials.
‘As for the game, we were comfortable and should have been 5-0 up after 10 minutes.
‘We didn’t take our chances and – no disrespect to Blackfield & Langley – it was probably too easy for us.
‘We got the one thing we wanted, though, which was the win.’
The Hawks imposed themselves on the game immediately.
Jake Newton’s ball over the top put Ollie Palmer clear but the striker lobbed his effort wide of the post.
Palmer was wasteful again, dragging another effort wide of the upright with just the keeper to beat.
But the Hawks finally broke the deadlock on 18 minutes when Jones latched on to a through ball and hoisted his shot over the keeper and into the empty net.
He then grabbed his second on 34 minutes, heading home a lovely Newton cross.
The Wessex League premier division hosts were being outclassed.
And the visitors’ task was made even easier two minutes before half-time when the home side had Joe Bye sent off for dissent.
Blackfield & Langley were no better after the break, struggling to get out of their half as the Hawks dominated possession.
On the hour Gale made his first change, sending Lee Peacock on in place of Palmer.
And the one-way traffic continued as Jones was only denied his hat-trick by a good save from Blackfield goalkeeper Jamie Bray.
On 70 minutes, though, the Hawks were also reduced to 10 men.
Holland received a yellow card for fouling Warren Hunt on the edge of the box and was then shown a straight red for dissent.
The Watersiders began to see a little more of the ball and substitute Sam Elson headed narrowly wide from a corner with five minutes left.
But in the end it was a comfortable passage through for the Hawks.
Moneyfields joined them in the hat for the fourth round following a 4-2 triumph at Alton.
Two Steve Hutchings strikes sandwiched a Jamie Hore effort, after Jake Slater had given Moneys the lead.
AFC Portchester also kept their cup dreams alive with a 5-1 victory over Ringwood.
A brace from Zac MacGregor and one from Jay Ripiner set the hosts on their way in the first half.
Blackfield & Langley: Bray, Settle, Lucas, Bye, Vickers, Aslett, Johnston, Newman, Willett, Hunt, Soetan. Subs: Elson, Ngwa, Clarke
Hawks: Beazley, Newton, Ryan, Hopkinson, Holland, Pearce, Whyte, Ramsey, Jones, Palmer, Hinshelwood. Subs: Woodford, Igoe, Peacock, Geteski, Norton
Referee: W Ball (Southampton)