Carlos Mendes Gomes scored the only goal of the game from the spot during the second half of extra time.
There was little to separate the two sides during 90 minutes though Bobby Madley's decision not to give a penalty to the Welsh side in the first half was a point of contention.
Kyle Letheren came to punch away a cross, missed it and seemed to instead make contact with Scott Bennett, though nothing was given.
The Shrimps penalty was also controversial, with question marks over whether the foul on John O'Sullivan was either in the box or a foul at all.
Having also lost out in the League Two play-off final in 2019, Exiles manager Flynn wants to see technology used in future.
He said: "I said it two years ago, you've got to have VAR at these big games.
"They'll come back with the excuse that we haven't had it all year so it's unethical. That is a load of rubbish.
"There is not one game throughout the season that determines what division you are in other than the play-off final. That is a cop out.
"They are two terrible decisions and I'm gutted for the players, the club and the supporters.
"We'll have a sorry in the next few weeks from the referee's report that they do. It's too little too late."
Although the 40-year-old couldn't hide his frustration, Flynn gave full credit to the victorious Shrimps.
The Welshman felt it was important to remain classy in defeat and was a credit to his club.
He said: "I'm devastated, I'm hurting but I want to give Morecambe Derek Adams and their staff and fans congratulations.
"They've had an outstanding season and they need to enjoy the moment.
"I think it is always good to have dignity in defeat and they've had an outstanding season so congratulations Morecambe."
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