"We wondered post surgery what it was going to look like, how his elbow was going to react to the strain and stress, but it was his heart and head that didn't react the right way in this match".
Djokovic was makings his first appearance since being stunned by Hyeon Chung at the Australian Open.
Meanwhile, Federer progressed to Round of 32 of the ongoing ATP Masters event in California.
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"It felt like first match I ever played on the tour", Djokovic said. 'I just completely lost rhythm, everything, struggled a little bit with the health the last couple of weeks.
Kasatkina has beaten all four of the current Grand Slam champions in the a year ago: French Open victor Jelena Ostapenko, Australian Open victor Caroline Wozniacki, Wimbledon victor Garbine Muguruza and now Stephens.
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Djokovic scrambled to win the second set, but looked rusty on stadium court, making 62 unforced errors compared to 29 for Daniel.
In other matches, Borna Coric of Croatia upset No. 13 Roberto Bautista Agut of Spain 6-1, 6-3; Jeremy Chardy beat No. 20 Adrian Mannarino 7-5, 4-6, 6-1 in an all-French matchup; and No. 11 Pablo Carreno Busta of Spain defeated Daniil Medvedev of Russian Federation 6-1, 7-5. "I have been sick for over a week and tried everything I could to get better".
He will face 25th-seed Filip Krajinovic in the third round.
Yuki Bhambri of India pulled off a surprise when he toppled ninth-seeded Frenchman Lucas Pouille 6-4 6-4.
However, Daniel bounced back as he won the third set comfortably to clinch the match.
Federer, five times victor of this tournament and defender of the title, invested less than an hour to win 6-2 and 6-1 against the number 28 in the world, reports Efe. "Back in the day, I used to play six matches in a row". Fifth seed Karolina Pliskova too needed three sets to reach the fourth round but the French Open titlist Jelena Ostapenko bowed out.