The Saddlers' final outing of 2021/22 saw the rampant Robins enjoy exactly the day they hoped for, with the visitors winning 3-0 to seal a play-off place.
They took the lead after just three minutes through Harry McKirdy and put the game to bed before half-time as Jack Payne then struck twice.
"It was a terrible first half. We did everything we told them not to do," said Flynn.
"We gave them the lead after three minutes, and that just made the whole day even tougher.
"It got their confidence up and their fans going, and all three goals were preventable from us.
"From Swindon's perspective, they're good goals, but from ours, they're terrible.
"We were wide open. We got sucked in and left runners. It was a calamitous first 45 minutes.
"In the second half, we huffed and puffed. We actually had more shots than Swindon, but we just don't take our chances. That's something I'll be working on.
"We should have scored a goal in the second half, to make it interesting at least.
"Our supporters deserved us to make a game out of it as they were absolutely superb."
Walsall finished 16th in League Two after a dismal display, while Swindon are due to take on Port Vale in the play-offs.
One of the few positives on the day for the Saddlers saw Mat Sadler given a late cameo in what was his final game for the club.
Having served as player-coach in recent years, his playing contract ends this summer, and he appears set to move into a full-time coaching role with the club.
"He's had a fantastic career. He's a great bloke," said Flynn.
"I've just said 'welcome to the dark side' with the coaching.
"He's done his family proud and had an extremely successful career. It's what dreams are made of.
"It was the least I could do as he's an outstanding lad, and I've got a lot of time for him."
Flynn is now keen to get stuck into recruitment over the close season as he added: "I can't wait. We've already got four or five over the line, so I've started early.
"We've just got to crack on as there's going to be a big overhaul.
"In a way, that result has helped me. If you beat Swindon and finish 13th or 14th, your judgment starts getting clouded.
"But the brutal truth is we've finished 16th, and that's not good enough."