Fresh off his honeymoon and with his first child due, Djokovic went out to eventual winner Jo-Wilfried Tsonga in Toronto last week.
He had hoped to improve in this week's tournament, particularly as it's the only one of nine Masters 1000 events to elude him.
Read: Djokovic beaten in Toronto
Djokovic has been a four-time runner up on the hard courts in Ohio and lost to John Isner in the quarterfinals last year.
This time around he did not even get to that stage, losing control of his match against Robredo after losing a tight first set tiebreak 8-6.
Djokovic had actually retrieved an early break to level at 4-4 but could not take full advantage. A single break of service in the second set was enough for Robredo to close out a memorable win.
"Just many, many, many things are not clicking these two weeks on hard courts," Djokovic told the official ATP Tour website.
"It's unfortunate, but it's more than obvious I'm not playing even close to what I'm supposed to play. I have to keep on working and trying to get better for U.S.Open," added the Serbian.
Earlier, Isner had two match points against former Wimbledon and U.S. Open champion Andy Murray before the Briton emerged the winner in three sets.
Read: Djokovic revels in Wimbledon victory
Murray, who has slipped to eighth in the world rankings after having back surgery in 2013, eventually prevailed 6-7 6-4 7-6.
America giant Isner had the match points on Murray's service as he trailed 5-6 in the deciding set, but could not capitalize on his opportunities.
Murray took control of the subsequent tiebreaker and won it for the loss of just two points to go into the last eight.
"I played very well," Murray told Sky Sports. "This is a big win for me as he (Isner) plays extremely well here."
In the women's tournament at the same venue, world number one Serena Williams maintained her hopes of a first Cincinnati title with a straight sets win over Italy's Flavia Pennetta 6-2 6-2 to reach the quarterfinals.
"I got an early break and just didn't let go," Williams told the official WTA Tour website.
She will face Serbia's Jelena Jankovic for a place in the semifinals after the eighth seed later beat Sloane Stephens of America 7-6 6-4.