The Bees tasted defeat for the first time this preseason after defeat at the hands of Concord Rangers.
Barnet started well, with two chances in the opening minutes. First, Jack Taylor shot wide of Wells' post before Shomotun fired wide shortly after.
Jordan Cox headed wide of Stephens' goal before he broke the deadlock in the 12th minute.
After a good cross from the right flank, Cox, unmarked, headed home to give Concord an unlikely advantage.
Shaq Coulthirst, making his first Barnet start, had an attempt in the 22nd minute but he was flagged offside.
Wells was to remain unbeaten this half, deny further shots from Coulthirst and Akpa Akpro.
After the break, Barnet were unlucky not to tie the game after Shomotun's shot cannoned off the post. Clough's follow up was saved and then Coulthirst's attempt was cleared off the line.
Concord doubled their advantage in the 73rd minute in similar circumstances to their first goal. A cross, this time from the left wing, found Taaffe unmarked who headed home with ease.
The Bees had the ball in the net five minutes later, but Akinola was flagged offside.
In the 85th minute, Justin Amaluzor pulled a goal back with a cool finish after bringing the ball under control with his chest.
However, with one minute left on the clock, Rangers secured the victory after Kyron Farrell was allowed time to volley home from all of 20 yards.
Barnet will now move all attentions to next Saturday's opening league fixture away to Forest Green Rovers.
Barnet: Stephens, Johnson (Amaluzor 77), Clough, Santos, Campbell-Ryce, Coulthirst (Tutonda 61), J Taylor (Trialist 45), Bover (Vilhete 45), H Taylor, Shomotun (Akinola 61), Akpa Akpro.
Subs not used: Ross, Akinde, Fonguck, Mason-Clark, Smith.