The title chasers went down 2-0 at in-form Bromley on a night when they never really got going.
They failed to close the gap on leaders Leyton Orient after recent defeats to Salford City and Dover Athletic.
Wrexham didn’t make use of their game in hand but they are only points points off the pace despite slipping to fourth place.
Barrow told the BBC: "We've been on this 3G surface three or four times this season and we learnt from the Sutton one.
“We talked about it beforehand today - everybody thinks it's going to be a beautiful football game because it's flat, but it's not.
"It's about competing for the ball all the time and we didn't do that in the first half.
"In the second half we did and gave ourselves a glimmer of hope, but obviously we didn't create enough."