The French winger scored three times inside the opening 32 minutes, and the victory was enough to secure the Shrimpers at least a place in the play-offs.
Mohsni opened the scoring in the 11th minute when he fired home from six yards after Neil Harris' 20 yard free-kick had bounced back off the left-hand post.
Moments later, Mohsni headed a right-wing cross from Harris only inches past the right-hand post before he fired wide of the left-hand post from close range.
Mohsni remained a constant threat and doubled Southend's lead in the 25th minute with a diving header from Ryan Hall's left-wing corner.
Exactly the same combination then led to the Shrimpers making it 3-0 just seven minutes later as Mohsni again nodded home another Hall corner. And not even a more spirited second-half display could rescue a disastrous first game back in charge of Barnet for Martin Allen.