Stokes lost control of the ball before the catch was complete.
The incident happened in the last over before lunch when Moeen Ali’s delivery hit the glove of Smith as the latter came forward to defend.
The ball looped to Stokes at leg slip and the England captain plucked a one-handed stunner above his head. However, he dropped the ball during the celebration as his palm hit his knees.
England opted for a review after the on-field umpire declared it not out. After watching the replay, the third umpire upheld the original decision, citing that Stokes wasn’t fully in control of the ball during the catch and Smith stayed not out.
Chasing 384 to win, Australia were 238/3 at lunch on Day 5 with Smith (40*) and Travis Head (31*) unbeaten in the middle.
The visitors need 146 more runs to clinch the Ashes 3-1, with rain threatening to play spoilsport as well.