The Red Devils boast four wins from their last seven away games, but only one victory in the last 11 matches at the Broadfield Stadium has seriously dented their bid to make a top-six challenge.
Barker said: "This is our first-ever season in League One and we're making good teams shut up shop when they play against us.
"We were in the Conference two years ago, so when you have teams come and try to stop you playing it speaks volumes to how well we've done."
Crawley are having to make do without three of their best players in Kyle McFadzean, Josh Simpson and Billy Clarke and Barker feels it would be a test for any side in the division to have such important players out of action.
He added: "We're really taking it to teams, but unfortunately people are shutting up shop.
"We had loads of possession, but we are never a team who will lump it. We could have done with ugly goals.
"It was a good chance, but we'll keep going until it is not mathematically possible.
"Of late, we have deserved more from the games that we have drawn.
"For this club to be where we are is fantastic. It's just disappointing we are not getting what we deserve."