The Perth side played the final 12 minutes of the match with 10 men after Liam Craig was sent off for a second booking.
Despite their numerical superiority, however, St Mirren could not make the breakthrough.
Goodwin said: "Frustration is the key word tonight.
"Sometimes when teams go down to 10 men it actually makes it more difficult to break them down. St Johnstone defended really well for the last 10 minutes of the game.
"My disappointment is that we didn't get the ball forward early enough in that period. We got into some good areas but didn't put enough crosses in or give our strikers something to attack.
"We've hit the post a couple of times and Zander Clark has made some fantastic saves.
"You've got to give credit to St Johnstone. They'll be happier with the point than we are.
He continued: "That's two games back-to-back where we've not been able to hit the back of the net.
"We had that conversation after the game with the players. People have to step up and make that killer pass or produce that bit of magic that can make the difference between the two teams.
"We couldn't break down Aberdeen and it was the same with St Johnstone. But we knew we wouldn't be able to just turn up and roll them over."
Goodwin insisted he was not overly disheartened by Hamilton's win over Rangers which closes the gap at the bottom of the table.
He added: "Fair play to Hamilton. That's a fantastic result for them. Brian Rice will be delighted as anything you get from the Old Firm are bonus points.
"But I'm not really concerned about anyone else. Genuinely I'm just concentrating on what we can do."
St Johnstone manager Tommy Wright resisted the urge to criticise referee Euan Anderson for Craig's red card.
He said: "There was hardly a bad foul in the game. But we end up with a player send off for two innocuous challenges.
"I've said enough about referees in the past, so I'll make no comment."