Barnet were forced into a change very early on when Craig Robson picked up a knock and had to be replaced by Dan Sweeney.
A mix-up at the back for Ipswich gave a trialist a chance for Barnet, but he put the ball narrowly the wrong side of the post.
At the other end, Jordan Roberts also saw a shot from the edge of the box go agonisingly wide of the upright.
Before the break, Jack Taylor lifted in a great free-kick but there was nobody running in to get on the end of it.
Martyn Waghorn lined up a free kick from 20-yards out but his shot hit the side netting.
After the restart, a trialist hooked an effort high over the bar after turning the Ipswich defence.
Mark Cousins was forced into action and produced an excellent save to stop Waghorn’s free-kick from nestling in the top corner of his goal.
The hour mark saw the much anticipated return of Dave Tarpey from injury but he had to watch as Ipswich took the lead 8 minutes later.
Myles Kenlock unlocked the Bees defence before firing low past Cousins into the bottom right corner.
As the game came to a close, Barnet had their best opportunity but Dan Sweeney had his header from Shaq Coulthirst’s pin-point cross well saved by Gerken.
Barnet – Cousins (Trialist GK, 84), Alexander, Reynolds, Robson (Sweeney, 5), Adams, Sparkes (Kyei, 77), J. Taylor (Coulthirst, 60), Fonguck (Boucaud, 74), Trialist One (Mason-Clark, 64), Trialist Two (Tarpey, 60), Payne.
Unused – Johnson
Attendance – 922
Referee – Will Finnie