Alex secured seventh place with a final day draw at home to Aldershot, a 16th game unbeaten in a relentless late-season surge from Steve Davis' side.
By contrast, Paul Sturrock's Shrimpers have chased automatic promotion for the majority of the campaign and were only denied when Crawley secured a 1-0 win at Accrington on the final day.
"The pressure was on a little bit on Saturday because it was in our hands," said Dugdale ahead of this weekend's first leg at Gresty Road. "We're the underdogs now, but everyone is raring to go.
"They beat us twice this season. When I say we're underdogs, we're not fearing them by any means. The pressure's off us, the pressure's right on them.
"They obviously were trying to go for automatic; we sneaked in at the back door right at the end. So the pressure's off us, everyone's confident enough and I'm sure Steve and Neil (Baker, assistant manager) will have a plan so we can go and get a result against them."