The attendance of 13,251 is the highest in npower League Two this season and the vast majority were delighted to see on-loan Crystal Palace forward Jason Banton's goal wrap up a third straight win for the hosts.
Sheridan said: "That result was for the supporters. The support they get for a team fighting relegation is unbelievable. I just can't believe it, so that result was for them."
Banton struck from outside the area after cleverly beating two City defenders before sending a low angled drive past Artur Krysiak and in off the post on the stroke of half-time. Banton has now scored six goals in 11 Argyle appearances since being drafted in by Sheridan.
Sheridan said: "It was very pleasing. I think we deserved to win. I think it was a very good performance in a big derby game against against a very good passing team who have had some excellent results away from home.
"If you let them play they are one of the best teams in the division and we made that clear to the players before the game. But I thought we kept them quiet for most of the game. I thought they started well, their first five minutes worried me the most and (Jamie) Cureton got a chance out of nothing.
"Full credit to my players, their effort to try and get something out of the game - to win it - has been brilliant. To be fair to them it has been since I have been here and we have just got to carrying on doing it."
Philosophical City boss Paul Tisdale said: "My first thought is that it is disappointing of course and my second thought is moving on to the next game, which we have to do.
"It's the business end of the season. It's good for me to note this game, and have opinions and an objective view and bank it for the future but what we need to do is move to the next game.
"We have got six games to go, 18 points at stake and as much as I feel miserable now, it's good for me to acknowledge that - understand why and how - and move to the next, which we have to. I didn't think we played well enough to win the game. Our game wasn't cohesive enough."