Gills striker Adebayo Akinfenwa slotted home from close range after 40 minutes following neat interplay between Myles Weston and Danny Kedwell before Bees goalkeeper David Button denied the same two players from doubling the Kent side's advantage.
For Brentford, Harlee Dean's header failed to trouble Nelson after he latched on to George Saville's free-kick in the opening minutes, while Chris Whelpdale's instinctive block denied Clayton Donaldson an injury-time equaliser shortly before Farid El Alagui earned the Bees a point with a last-gasp strike.
It is a first point of the season for Gillingham, but it was not the win manager Martin Allen was looking for against his old club and he left post-match media duties to Schofield.
"Brentford are a highly-fancied team, but to us it's irrelevant who is in the other dressing room," Schofield said.
"We have to perform to our level, and if we do that, we'll give ourselves a chance of picking up points every week. I think we've done that.
"The intensity was there and the way we passed the ball and our tempo was there to be seen.
"You're always disappointed to concede a goal and if we had conceded with half an hour to go, it wouldn't have felt like it feels now.
"The confidence among the players is great, their spirit is still high. I think when you look at the teams in League One, you know every game is going to be hard.
"I think we've adapted to the level of competition well and we've had good spells in every game we've played this season."