Paul Cox, the Bluebirds manager, was frustrated his side let two points slip through their fingers in midweek.
After going 2-0 up they then lost Jimmy Dunne to a red card. Barrow couldn't hold on and Solihull Moors went 3-2 in front.
But a last minute leveller handed them a 3-3 draw in a turbulent but exciting encounter.
It means Cox's team couldn't take full advantage of their excellent victory against Woking last weekend.
Barrow's long trip to Dover will only end well if they improve their control over matches.
“What we need to do is have an understanding of game management, and for 20 minutes after we lost Jimmy on Tuesday we lost our game management," said Cox.
"We lost the ability to close a game down, the ability to keep a clean sheet. These are all the learning curves we need to go through.
“The sooner we do that – because we will have nights like Tuesday – the better. It’s going to be a long, long season, and we need to have an understanding of closing games down, especially when you are away from home and 2-0 up.
"We should have won that game 2-0, and I would have been happy with that."