The British No 2 is yet to post a win over a top-10 player and this was another match where he showed a lot of promise, but failed to take advantage of half chances.
Edmund matched Cilic in the second set and threatened to break the big Croatian’s serve several times but could not get over the line.,
Cilic then came out on top of the deciding tie-break to win 6-3 7-6 (7/5).
Also out is Australian Nick Kyrgios, who courted controversy again by retiring after losing the first set of his opening-round match against Steve Johnson.
Kyrgios was banned for showing a lack of effort and arguing with the umpire and fans during a second-round loss to Mischa Zverev at the same tournament 12 months ago.
Kyrgios did not appear injured and did not seek medical help before abruptly pulling the plug after Johnson claimed the first set 7-5 on a tie-break.
Both the American and umpire Fergus Murphy were bemused by Kyrgios’s sudden retirement, which he later blamed on a stomach bug.
The 22-year-old cut a distracted and grumpy figure throughout and complained about Murphy several times.
When he was given a point penalty during the tie-break for an audible obscenity, having previously received a warning for angrily smashing two balls out of court, Kyrgios was heard saying he would quit if he lost the tie-break.
Explaining his decision, which drew boos from the crowd, Kyrgios wrote on Twitter: “I’ve been battling a stomach bug for the last 24 hours and I tried to be ready, but I was really struggling on the court, which I think was pretty evident from the first point.”
British No 3 Naomi Broady was unable to take advantage of her lucky loser spot as she lost in the opening round of the Upper Austria Ladies Linz to Bulgarian qualifier Viktoriya Tomova 3-6 7-6 (8/6) 6-4.
Andy Murray is set to compete in the Australian Open next January, according to the tournament director Craig Tiley.
The British No 1 has been sidelined since limping out of Wimbledon with a hip injury in July and, although he has not officially confirmed it, he is unlikely to play again this year.
Serena Williams, 23-time grand slam champion, appears set to return to defend the title she won while eight weeks pregnant with her first child, Alexis.
Prize money for next year’s tournament will rise with the men’s and women’s champions each earning £2.3m.