Wrexham were undone by two goals from Toby Little inside the first 10 minutes and their already uphill battle was made worse early in the second half when Lamine Sakho received a straight red card for a head-butt on Esmond James.
The Dragons are nine points above the Blue Square Premier relegation zone and 13 points behind Luton Town in the last play-off place.
"We started poorly and in football you can't start poorly and expect to turn the game around straight away," added defender Westwood.
"We ended up getting what we deserved which was nothing.
"We just need to get it out of our system as soon as possible. Too many of us had bad days.
"Sometimes you can afford to carry one or two but certainly the numbers we tried to carry today, you can't do it."
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