Speaking on BBC Radio Sheffield, the former Owls defender criticised the team following their 3-0 defeat to Plymouth Argyle.
After a narrow defeat to Watford, Danny Rohl took charge of his second game since arriving in Yorkshire.
Sheffield Wednesday needed to close the gap on Plymouth, who sat just above the relegation zone ahead of Wednesday’s clash.
The Owls found themselves behind thanks to an impressive free-kick from the Pilgrims, though the visitors still looked very much in the game.
However, a mistake from Pol Valentin gifted Plymouth their second goal, which Smith claimed ‘killed the game’ at Home Park Stadium.
Smith said: “What went wrong really was the second goal – it just kills you. We were more than in the game and had restricted Plymouth to one shot that hit the outside of the post.