Motherwell dominated the first half but only had Liam Donnelly's penalty to show for their superiority and Saints took less than five minutes of a much-improved second-half showing to level through Jon Obika.
The visitors sealed their second victory at Fir Park in eight days when Ilkay Durmus fired home with four minutes left.
"The first half we looked a shadow of the team we were in the first 45 minutes last week," Goodwin said.
"Motherwell deservedly went in in front and but for a good save by my goalkeeper it could have been worse.
"We had to have a strong discussion at half-time, I asked for a bit more aggression all over the park, I asked them to play more directly and get the ball forward a little bit earlier, and it worked to our advantage. The majority of the game was played in Motherwell's half in the second half.
"Early on in the season that's a game we might have been happy to take a point from but we felt Motherwell were there for the taking.
"It is a massive result in the end and those three points could be huge."
Motherwell have now not won in eight games and they missed the chance to move four points clear in third place.
Manager Stephen Robinson said: "We should have been out of sight and it could have been three or four nil. But St Mirren were always going to come into the game. They were clinical and we weren't.
"I still have a lot of faith in these boys. We've been here before, a sticky spell, you keep believing in what you do. It's up to me to get their confidence back up again.
"There is no point in me ranting and raving at them. They are just low on confidence. It's time for an arm around people and sticking together.
"I won't lose my belief in them. It's time to give them a cuddle."
David Turnbull made his first appearance of the season following knee surgery as a 71st-minute substitute but Motherwell could not utilise him as they pressed before the late blow.
Robinson said: "It was good to see David back. That's probably the limit of where he is in terms of game time.
"We've got a free week now where we can get him fitter. But David is not ready to start football matches.
"Believe me, if he was ready, he'd be starting, because I could think of no one better to start for us.
"The long-term future of David Turnbull and Motherwell is more important than a short-term fix."