County created chance after chance but failed to capitalise and Saints took full advantage with a smash-and-grab win thanks to a dramatic injury-time penalty by Stephen Thompson.
Martin Woods fired County ahead from the penalty spot in the 31st minute but it was all-square eight minutes later when Stephen Mallan scored with a deflected drive.
However, as the game went into stoppage time, Mark Brown charged from his goal to upend Saints’ sub Lewis Morgan and Thompson rolled home the spot-kick.
Teale said: “The fans deserve that, having come a hell of a long way under the circumstances, and they demand a performance.
“They’ve put themselves out of their way to come up here and they’ve got to see something.
“Don’t get me wrong, we rode our luck at times in the game. I felt everybody throughout the team did well but my goalkeeper and my defence were excellent today.”
St Mirren’s relegation from the Scottish Premiship was confirmed by Motherwell’s defeat of Kilmarnock on Friday night, but Teale is hoping victory over County will see them end the campaign on a better note.
He said: “I’m a big believer in you deserve to be where you are and we’ve not been good enough throughout the whole season, but we just need to go and put in another couple of performances like we did today.”
County boss Jim McIntyre felt his side, who are not yet safe from avoiding the relegation play-off, created enough opportunities to win the game.
“I think the chances we created were clear-cut and we should have been out of sight,” he said. “If you don’t do that then the opposition have always got a chance of getting back into the game.
“I’m not displeased at how we played at all. I thought we played some great stuff into great areas and we were wasteful in front of goal.
“The thing we’re looking for is not to lose the match. I thought we could’ve managed the game better. We were chasing that win and at times it left us exposed on the counter-attack.
“Mark Brown has to stay in his goal, it isn’t on for him to come. It’s good play from St Mirren’s point of view but we were ragged because we were going all out to try and get that goal, and we needed to manage that a wee bit better in the same way we were doing in the first half.”