A female fan was hurt as a result of this as the bottle struck the woman on the head.
A spokesman for West Yorkshire Police said: "We have spoken to the match commander at Elland Road and are aware of the incident that took place."
Peter Reid, who did not see the incident involving Smith, looked back on yet another defeat with cold realisation.
"It's been a difficult time at the football club recently, but the spirit among the players and supporters has been fantastic and that's one thing that money can't buy,'' said Reid.
"We have to take it as a positive, a strength, and move onto the next game which is going to be a very difficult one against Arsenal.
"But I'm sure things will change if the players keep on giving me the football and attitude they've shown in the last two games, but it's a difficult time at the minute.
"We are not getting the rub of the green at the moment and the players must be scratching their heads wondering why they can't get a break.''