Lee Williams' 34th minute cross found Tony Naylor, but his close-range shot was blocked by Musselwhite.
City's best opening came five minutes before half time. Van Blerk crossed to Lightbourne, who set up David Norris but he fired just over.
Both sides registered shots in the opening minutes of the second half. Robins 'keeper Steve Book caught Gary Alexander's shot from the edge of the area, while Russell Minton put one over from distance two minutes later.
Cheltenham forward Julian Alsop went into the book in the 57th minute for a foul on Jason Van Blerk, and Richard Sneekes' name was taken down a minute later for diving. Sneekes was substituted five minutes later, with Theo Whitmore coming on.
The home side continued to come forward, and the goal eventually came 20 minutes from time. Minton's corner was met unchallenged by John Brough, who headed past Musselwhite.
Five minutes later Norris won a free kick 25 yards out. However, Alexander's shot hit the wall and went out for a throw-in.
David Beresford replaced Kyle Lightbourne 10 minutes from time. Norris shot over from long-range, and Mohan headed wide from a corner, but the equaliser wouldn't come.
Johnsson went off for Ben Petty in stoppage time with a knock, before Mr. Warren blew for full time on this lacklustre game.
City line-up (4-4-2): Musselwhite; Edwards, Whittle, Mohan, Van Blerk; Williams, Sneekes (Whitmore), Norris, Johnsson (Petty); Alexander, Lightbourne (Beresford).
Un-used subs: Glennon, Holt.