Argyle captain Conor Hourihane cancelled out Jake Hyde's 21st-minute opener with a cracking 25-yard drive at Home Park on Saturday before on-loan Ipswich forward Ronan Murray finished clinically from 10 yards to delight Sheridan.
"Barnet scored against the run of play and in the position we are in, we could have let our heads drop but instead of that we rose," he said.
"That spoke volumes for our character and we will need more of that in the coming weeks.
"Conor got a great goal to get us back in it and then Ronan has got his goal, which pleased me because he's been great since he's been here. He's been in and out of the team but still kept his head down and he got his reward. The whole team did.
"I thought we backed off a little bit after we scored but then we finished strongly and obviously I am delighted we are off the bottom.
"It's only one game, one win but when you are bottom of the league and you get 8,000 plus fans in, then it's nice to get the three points for them.
"I was nervous before the game but I don't think the players showed it and obviously we all know what's at stake and the importance of trying to get three points.
"That's the way I want us to play, show a bit of endeavour and a will to win. We passed it when we had to pass it and we were a threat.
"We had good opportunities to score more goals and Barnet are a good team. They have had some great results in the last six games, when they have played teams off the park, but I thought we did that to them at times."
