Conor Sammon put the visitors ahead before Craig Noone salvaged a point for the npower Championship leaders.
A point stood as an excellent result for the injury-hit Rams, who only had five players on the bench, but Garner was disappointed after seeing a Chris Martin strike ruled out for offside and a penalty appeal for handball against Ben Turner rejected.
Garner said: "With the disallowed goal I had a word with the assistant referee at half-time, which is not the best of times, but I asked him if he was 100 per cent happy with his decision and he said he was.
"I have seen the replay and Chris is half a yard onside. Chris walked in at half-time and said there was no way he was offside, and he was right. As a striker you know if you are onside or offside."
On the penalty decision, which occurred when Turner flung himself at Jeff Hendrick's shot, Garner added: "How many times do you see them given? When you are watching Match of the Day or the Football League show on TV every weekend you see them given week in, week out.
"The referee told the players it hit his hand so I don't understand why he didn't give it."