Playing with depth from the baseline to push Draper back, particularly putting scrutiny on his opponent's backhand, worked a treat.
Draper was unable to get into position to execute his forehand and, although finding his first serve helped survive three break points at 4-3 down, he finally lost serve at the end of the opening set.
With the clouds gathering overhead, and the atmosphere becoming gloomier, Draper lost serve again early and it proved to be the decisive break in the second set.
Draper is still waiting for his Murray moment at Wimbledon – the one where he achieves the impossible at the All England Club and causes waves across the nation during a primetime summer slot.
Murray-mania exploded when the Scot fought back from two sets down against Richard Gasquet in 2008.
If Draper had turned things around against Cilic, it could have been a similar type of moment for him.
There was a brief glimmer of hope as Draper was able to use his forehand to greater effect in the third set, but any hopes of a memorable comeback were quickly extinguished.
Draper's exasperation continued to show in the fourth set - particularly with the electronic line-calling system which has replaced human line judges - and he was broken when serving to stay in the match after he disputed another decision at 15-0.
"I don't think it's 100% accurate, in all honesty," he said.
"A couple of the ones today, it showed a mark on the court. There's no way the chalk would have showed.
"I think it's a shame the [line] umpires aren't involved."