Recalled attacking midfielder Lewis Alessandra came closest to breaking the deadlock against County when he forced keeper Lenny Pidgeley to make a double save in the 32nd minute.
Early in the second half Ismail Yakubu looked set to convert from close range after a fine cross from Ryan Jackson, which acted as a spur for the home side with danger man Alessandra firing high and wide when well placed.
The game required 11 minutes of stoppage time - played in a torrential downpour - following a 75th minute floodlight failure.
Newport edged up a place to ninth while Argyle remain 19th without a win in seven games.
Sheridan said: "I am in talks with a club about bringing someone in because I just feel we need a lift. Everyone knows what the problem is; we aren't scoring goals.
"I think a draw was a fair result, I don't think either team was better than each other. They are well organised, compact and played a similar system to us.
"I thought we started really well, the first 10-15 minutes. Then I just felt we didn't keep possession of the ball in the final third or opposition's half for long enough periods. I think that was our biggest downfall tonight.
"Obviously the conditions got a bit difficult in the end but I think the pitch was beautiful (at the start).
"When we did go forward it was coming back at us. Even from keeper's kicks the ball is coming back to us too easily. I just think that we have got to work a lot harder to create opportunities and openings, cause the opposition more problems.
"Listen, we all know the problem is putting the ball in the back of the net. I thought it was a scrappy game but we know the importance of trying to win the game and we haven't, we've had another blank. It's another disappointing performance, no goals, it's a big problem."