Coric, who lost in the second round of qualifying to Mikhail Kukushkin, got into the main draw when Richard Gasquet withdrew. "I was a little bit surprised but he is a great champion and he'll be back for sure". However, an unforced error from Murray saw him send a cross-court forehand wide and gift Coric a chance to serve out the match.
"I think Feliciano played really well, especially in the second set", said defending champion Djokovic.
"That's concerning, so I need to think about exactly why that is, what I can do about it".
"It's not always the worst thing losing a match, but it's sometimes the manner of how you lose the match which can be concerning or disappointing".
World number one Andy Murray crashed out 6-3 6-3 in the third round of the Madrid Open on Thursday to 20-year-old Borna Coric as his hard start to the clay court season continued.
He will now take on Grigor Dimitrov or Dominic Thiem in the quarter-finals and Murray was disappointed with his performance.
Djokovic has had his own struggles of late.
Murray has also exited the Monte Carlo Masters prior to the quarter-final stage this year and suffered defeat in the semi-finals of the Barcelona Open, but he insists that confidence is not an issue heading into this month's French Open.
However, he believes he is making slow but steady progress after seeing off Lopez and a partisan crowd to reach the last eight.
"If you re playing against a Spanish player in Madrid, it s obviously a different game, it s a different feeling", said Djokovic. But you need to have the right sort of ideas, correct ideas, understand why you're in the position you're in.
However, Djokovic salvaged the game and then immediately broke the Spaniard's serve to set up a meeting with Japan's Kei Nishikori, who swept aside another home favourite David Ferrer 6-4 6-3.
However, Nishikori has only won two of their previous 13 meetings.
"Novak is someone that I don't have good record (against)", said the Japanese.
"Whereas today I didn't really do any of that stuff. I try to enjoy my big challenge tomorrow". The British player won the Madrid title in 2015.
Murray was beaten 6-3 6-3 by Coric, ranked 59th in the world, on Thursday. German Alexander Zverev also reached the last eight by beating Czech Tomas Berdych.
On the women's side, third-seeded Simona Halep of Romania reached the semifinals by beating Coco Vandeweghe of the USA 6-1, 6-1 in less than an hour.
She will now play Anastasija Sevastova of Latvia for a place in the final after she overcame Kiki Bertens of The Netherlands 6-3, 6-3.