The Aucklanders' final pass deserted them in the first-half for about 15 minutes of dominance.
The coach felt referee Paul Mason's penalty in the 15th minute was iffy.
Western Suburbs went up 1-0 in the 15th minute when defender Cody Doherty hacked down a player on the edge of the 18m box. Patrick O'Keefe put it past goalkeeper Damian Hirst from the penalty spot.
"That knocked the stuffing out of us because it was the first goal we had conceded. But, anyway, these things happen and they level out in football," he said.
Birkenhead won the title in 2010, were beaten finalists in 2011-12 and semifinalists last year.
"That's not bad for a little club," he said, adding they would have been disappointed had it gone into penalty kicks after dominating the second half.
Western Suburbs had come off a 4-2 penalty shootout victory over Western Springs in the semifinal in the morning, after the sides were locked 1-1 in regulation and extra time, while Birkenhead had beaten Ellerslie (Auckland) 2-0.
The Lloyd O'Keefe-coached red and blacks did remarkably well to push ahead 2-0 in the 25th minute from striker Tanashe Marowa when he poked the ball into the net following some deft passing in the box and some lackadaisical defence.
It wasn't until 11 minutes into the second-half that Birkenhead co-captain Elijah Neblett pulled one back to 2-1. He latched on to a through ball but Suburbs goalkeeper Mason Kelleher parried away the first wormburner. However, Neblett followed up with another shot that grazed underneath the crossbar.
Moses Dyer equalised 2-2 in the 50th minute from a pitch wedge-like shot at point-blank range as Suburbs watched like stunned mullets.
Stung into action with changes off the bench, Suburbs substitute Mike Faver nodded in an oblique-angle freekick in the 68th minute, after the initial header from Marowa, for a 3-2 lead but all the hugging and hoopla was premature.
Unfazed, Birkenhead made it 3-3 a minute later after keeper Kelleher fumbled in a challenge before Neblett found the net.
Suburbs players howled in protest but the ref didn't flinch, moving into five minutes of added time.
Six minutes into the 15-minute extra time, Tommy Miller scored the winner from a deft cross off the left flank.
Thirty seconds earlier Miller, making flower arrangements in the box, had butchered a one-on-one with the keeper, prompting O'Keefe to bark: "What else do you want [to score]?"
Hobson said the tourney was fantastic and they would return next year to defend their title.
O'Keefe echoed similar sentiments but said his boys were disappointed.
"We played some absolutely fantastic football, so I'm pleased from that perspective," he said, adding they were a technical side who just wanted to control the game's tempo.
"But they [Birkenhead] came back with some big boys with their physicality and determination, so I guess that was the difference."
In the all-Wellington satellite (lower-tier) final, Waterside Karori beat Island Bay 5-4 on penalty kicks after they were scoreless in extra time.
The lad who missed was inconsolable.
However, both sides gain promotion to the main draw next year.
