Southport took full advantage of ..the Linnets’ defensive frailties to bag a 2-0 lead in the opening 19 minutes.
Tommy Taylor’s troops, who had enough first-half chances to hold a lead going into the break, deservedly pulled a goal back before a controversial penalty decision saw the Sandgrounders restore their two-goal cushion, from which Lynn never recovered.
Manager Taylor said: “We were very poor as a team.
“We left ourselves with a mountain to climb straightaway by conceding silly goals.
“I’m pleased that it was a cup game and not three league points that we lost.
“If that had been -a league game then I would have been devastated by the way we played”.
Lynn began the brighter of the two sides with Carl Holmes being denied by the legs of Southport keeper Steve Dickinson.
The Walks outfit maintained their early momentum and in the 9th minute David Staff’s corner sailed over everyone before crashing against the bar.
The loose ball fell kindly to Holmes, whose follow up was cleared off the line by Farrell Kilbane.
Lynn were left to rue their early misses when Southport took the lead with their first chance of the match in the 16th minute.
Steve Daly set up Kilbane with a neat lob and Steve Wilson and his defence were no where to be seen as the brother of Everton star Kevin nodded the ball into the net.


Worse was to follow three minutes later when a static Lynn defence were found out by a Kevin Lynch cross and Daly turned the ball home.
To their credit, Lynn refused to surrender and were duly rewarded 10 minutes later.
A crisp move, involving Adam Jones and Chris Bacon on the right, resulted in an inviting cross for Danny Bloomfield to get the merest of connections.
Bloomfield’s shot was goalbound, but it still took a wicked deflection from Kilbane to see the ball cross the line as Earl Davis did his best to prevent a goal.
The pivotal point of the match came in the 32nd minute when top Southport scorer Terry Fearns was judged to have been up-ended in the box by Wilson, when the Merseyside hot shot had clearly been looking for a spotkick.
The forward picked himself up before blasting past Wilson and ending the game as a contest.
A professional Southport outfit frustrated the Linnets by keeping the ball in the second period and Taylor’s side returned to playing their long-ball tactics in a dire second half, where chances were few and far between.
The acrobatics of Wilson to foil Neil Robinson denied Southport a fourth shortly after the break, but the second half’ lacked the excitement of the previous 45 minutes.