The Sky Blues have been held to a goalless draw at the Hive in SkyBet League Two.
Max Biamou and Marc McNulty came closest for the visitors but Mark Robbins' side failed to find the breakthrough.
Jordan Ponticelli was handed his league debut for City on an afternoon lacking excitment in North London.
Biamou has been a constant in the City line-up ever since breaking into the side last month and came closest to opening the scoring in this one. Liam Kelly's long and floated free-kick met nicely with Biamou's head but the Frenchman's header sailed wide.
The Bees lead with former Shrewsbury forward Jean-Louis Akpa-Akpro in attack, and the pacey forward did not waste time in causing the Sky Blues problems. If it wasn't for a well time interception from Lia Kelly, his gently lofted lob would have almost certainly let Andre Blackman in one-on-one with Lee Burge.
It may have taken half an hour, but Coventry soon began to grow into the game. Jodi Jones flicked the ball long up the line for to chase down himself before picking out Devon Kelly-Evans charging through the centre. Kelly-Evans chopped his marker before forcing a strong block from Barnet defender Charlie Clough.
Jones again would be the creator for City's next chance. The teenager skipped a number of challenges before going for the spectacular with the outside of his left foot, but on this ocassion it sailed wide.
After the break, Mark Robins' side were attacking a stand full with a 1,390-strong Sky Blue Army, and were getting closer and closer to opening the scoring.
First McNulty found away to get goalside of Bees' left back David Tutonda before playing the ball across the area for both Kelly-Evans and Michael Doyle to have a stab at, but neither could make a true connection.
Next it was McNulty's turn to recieve the ball in the area, but the former Sheffield United man was crowded out and could not quite get his shot away.
With ten to go, Robins added Jordan Shipley and Jordan Ponticelli to the mix as City looked to grab a late winner. Biamou again came close when he skipped a challenge and fired a low effort acrosss goal and wide of the far post.
Liam Kelly was almot forced off with an injury early on in the second half, his thunderous volley stung the palms of Barnet 'keeper Craig Ross and started a flurry of Sky Blue chances as Biamou could only watch two of his efforts at goal scrambled away from the goal-line.
Attendance: 4041 (1,390 away).
Coventry City XI: Burge (GK); Grimmer, Willis, McDonald, Stokes, Kelly, Doyle, Dev.Kelly-Evans (Shipley '77) , Jones, McNulty Biamou.
Subs: O'Brien (GK), Davies, Stevenson, Vinceni, Beavon, Ponticelli.
Barnet XI: Ross (GK); Clough, J. Taylor, Almeida-Santos, Tutonda, Akpa-Akpro, Vilhete, Fonguck (Mason-Clark '67), Blackman (Shomotun 78'), Bover (Akinola '67), H. Taylor.
Subs: McKenzie-Lyle (GK), Nelson, Akinola, Kyei, Malakai-Mars.