The Robins fell to a 4-0 defeat away against Portsmouth in the Sky Bet League One.
Pompey grabbed three goals in short succession in the first half, putting the game out of reach from the Robins, before adding another late on.
A much improved second-half performance for Wade Elliott’s side ultimately proved not to be enough as they left without anything to show for their efforts.
Pompey came forward with the first attack of the game, Caleb Taylor was on hand to make a big tackle to deny Colby Bishop though.
The home side would break the deadlock early on, as Ryan Tunnicliffe’s curling effort from outside the box found the bottom corner of Southwood’s goal.
Michael Jacobs would double the lead for Pompey, drilling the ball past Southwood from inside the penalty area.
A third would come for Portsmouth, Ronan Curtis tapped home from close range after a low cross from Tunnicliffe.
Debutant Glen Rea started the second half well for the Robins, with his shot from range going wide of the post.
Cheltenham continued to come forward with Alfie May finding space out wide, whipping a ball to Broom who was judged to be offside.
Rea played a good cross into the box that was met by Charlie Raglan, whose header was blocked on its way to the goal.
The Robins had a golden chance to pull one back as the ball dropped to Aiden Keena whose effort went over the bar.
Despite a late flurry from Cheltenham, Pompey added a fourth with Louis Thompson scoring a goal from long range in added time.
Portsmouth – Macey, Ogilvie, Tunnicliffe, Bishop, Curtis, Dale, Morrell, Rafferty, Raggett ©, Jacobs, Towler
Un-used substitutes – Oluwayemi, Hume, Piggott, Scarlett, Thompson, Bernard, Lane
Robins – Southwood, Long ©, Raglan, May, Taylor, Ferry, Jackson, Bonds, Keena, Perry, Broom
Un-used substitutes – MacDonald, Brown, Sercombe, Barkers, Norton, Rea, Olayinka
Referee – L Swabey
Attendance – 17,504 (366)