Killie were lucky to only have conceded one goal during the opening 45 minutes at Tannadice.
Kilmarnock improved during the second period and substitute Gary Wales saw a late volley across goal stopped by an outstanding save from Grzegorz Szamotulski, but Jefferies was left to once again lament a lacklustre start from his side.
He said: "That is two weeks on the trot we have not started well and our performance between the first half and the second was night and day.
"There were a few harsh words said again at half-time and that is something we shouldn't have to be doing, especially after last week when we should have learned our lesson.
"I thought the application and dedication to get back into the game in the second half was there from the players, but we need to make sure we start games in the right way."