With the must-win game against Stuttgart in the Champions League looming, Smith admits Rangers took their foot off the pedal in the second half.
Smith said: "I think that's a natural thing, especially after scoring three goals and creating a number of opportunities in the first half.
"There was always likely to be a little bit of a drop in level in the second half and there certainly was that today."
He added: "We have built up a bit of momentum now and hopefully we can keep that going."
Kilmarnock manager Jim Jefferies said: "We started the game really well but you have to defend well and, after 10 minutes, we went to pieces and the defence was shocking.
"Young Ryan O'Leary had a torrid time in the first half and I thought about taking him off. But, credit to him, after taking a bit of a roasting at half-time, he stuck to his task better than he did in the first half.
"I don't think we have had as much possession at Ibrox, or worked the goalkeeper as much, but we can't defend the defence in the first half. We could have lost one or two more."
Jefferies also revealed striker Kevin Kyle is a doubt for next week's game against Hearts after being caught in the face by Rangers goalkeeper Allan McGregor's boot.