A superb first-half goal from Josh Robertson ensured Albion opened their Vertu Trophy campaign with a point at Barnet.
The Albion midfielder broke the deadlock shortly before the break with a swerving effort from 20 yards out but the Bees earned a share of the spoils through a second-half Callum Stead goal.
In a low-key opening to the game, it was the hosts who created the first opportunity when Dennis Adeniran headed over an Anthony Hartigan free-kick.
The Barnet striker also saw an effort deflected wide later in the half, and while the Seagulls struggled to create any clear-cut openings of their own, they did look a threat on the counter.
Joe Knight and Josh Robertson celebrate going in front at Barnet. đˇ by Simon Roe.
It was from one such break that the lively Robertson scored, showing good feet on the left before unleashing a superb effort that flew past Bees keeper Owen Evans.
The game came more to life after the break, with Nehemiah Oriola showing his pace before letting fly from distance.
Shane Nti also tested Evans, following good combination play with Belmont, while at the other end sub Oli Hawkins screwed an effort wide.
Barnet continued to press for the equaliser and it arrived in the 58th minute when Ben Winterburn split the Albion defence, leaving Callum Stead to round keeper Nils Ramming â who had been a first-half replacement for the injured Tom McGill.
The Bees continued on the front foot, with Ramming doing well to deny Stead following a scramble on the line, while Winterburn saw a curling effort hit the top of the crossbar.
Albion remained a danger on the break with sub Kofi Shaw shooting straight at Evans. The sub agonisingly failed to connect with an inviting Tyler Silsby cross moments later.
Albion were beaten 5-4 in the penalty shootout. đˇ by Simon Roe.
Sean Keogh came close to winning the game for the Seagulls in injury time, with his close-range header from a Silsby corner beaten out by Evans, and with the game drawn, a penalty shoot-out ensued. It was won 5-4 by the hosts to earn a bonus point on the night.
Albion: McGill (Ramming 33), Barclay, Simmonds, Atom, Tasker (Keogh 45), Knight, Albarus (Owusu 95), Robertson (Silsby 80), Oriola, Belmont (Shaw 61), Nti.
Subs not used: Mills, Mackley.