Pierre Emerick Aubameyang couldn’t score on his debut as the Blues badly underperformed in their Group E match.
The Croatian champions were the better team in the first half but Thomas Tuchel’s side pushed for an equaliser in the second period, coming closest when hitting the post through Reece James late on.
There will be huge disappointment to lose a game against the weakest side on paper in the group as matches against RB Salzburg and AC Milan are coming up next.
Nizaar Kinsella was in Zagreb to rate the Chelsea players...
Kepa Arrizabalaga - 6
Kepa made his first appearance since March 2, with doubts over both Edouard Mendy’s form and fitness following the close-run victory over West Ham.
He couldn’t do much with the goal which was well taken. Kepa was then forced into several saves from long-range shots including the Stefan Ristovski effort in the 56th minute.
Cesar Azpilicueta - 5
The Blues captain played very high up the pitch despite his centre back role to try to break down the Croatian champions.
Unforced error, Azpilicueta gave away a pass in the 33rd minute. He was substituted at half-time to get more attacking players on the pitch. He was perhaps unlucky to be hauled off.
Wesley Fofana - 4
On his Champions League debut, the 21-year-old was good in possession in a high line but got outpaced by Mislav Orsic who scored.
It seems to get to his head, with him overcommitting to challenges throughout the rest of the match to make amends.
Kalidou Koulibaly - 4
His intervention on the halfway line was weak and allowed Bruno Petkovic to flick the ball to fellow forward Orsic to score. He was booked for a heavy challenge late on.
Reece James - 7
One of the better Chelsea performers and he was able to show his superiority shortly after signing a new six-year deal worth £250,000-a-week. He seems the most consistent performer in Chelsea’s early season.
He came closest to equalising for Chelsea, hitting the post in the 86th minute.
Mason Mount - 5
Playing in an unusual no6 role during the first half and couldn’t impact the game in a disciplined role.He was then moved out to another unfavoured position on the left wing in a 4-4-2 and continued to struggle. He was booked for dissent and the opposition tried to get him sent off after his frustration began to show.
He did create the chance of the game for Havertz, crossing from inside the box. His long-range shot at the end of the match was well saved by Livakovic.
Mateo Kovacic - 6
Kovacic completed 60 minutes in what was an emotional homecoming at the club he broke through at and supported as a boy.
In front of most of his family and friends, the midfielder excelled until Dinamo scored and gradually saw his powers ebb away along with his teammates. He was far from the worst culprit in his home country.
Ben Chilwell - 4
Making his 50th start for Chelsea, the wing-back struggled badly in Croatia.
His night was summed up by a throw-in during the 54th minute which someone conspired to go in and then back out for a Dinamo.
Ultimately found himself substituted for Marc Cucurella.
Kai Havertz - 5
Havertz shot in the flashed wide and went out for a throw-in in the 10th minute. Still, he started incredibly brightly on the right wing, with a proper striker leading the line.
He had his side’s only shot on target in the first half, a tame effort that floated into goalkeeper Dominik Livakovic’s hands at a twelfth-minute corner.
His cross to Aubameyang in the 47th minute was dangerous after good wing play. But, overall, he faded as the match went on.Havertz’s header in the 82nd minute was the closest Chelsea came to scoring after Mount’s cross.
Pierre Emerick Aubameyang - 4
Aubameyang looked sluggish in Zagreb on his debut. It’s hardly surprising given his lack of training sessions in the weeks leading up to his transfer due to his injured face.
Still, it was a debut to forget when he often crossed instead of shot, found himself offside too often and didn’t really threaten to start with a goal.
Raheem Sterling - 4
Sterling found pockets between the lines and linked well with the two other forwards early on. He then gave the ball away for Mislav Orsic’s opening goal. He then played the second half in central midfield but roamed from his position to try to find openings. It didn’t work.
It was arguably his worst display since joining the club.
Hakim Ziyech - 6
Immediately came on and had a trademark long-range shot from 30 yards but it was easily saved. He played on the right in a 4-4-2 and then moved back to the left.He did lift the team with his ball-striking ability, but not enough to get the win.
Jorginho - 6
Played in a deep quarterback role with so many attackers on the pitch late on.
Armando Broja - 6
Broja threatened to get on the end of several crosses, just attempting to be the target man that Chelsea needed.
He couldn’t influence the game but his presence lifted the team.
Marc Cucurella - 6
Attempted a lot of overlapping runs to add width with Chelsea using inverted wingers on the flanks.
Christian Pulisic - 5
The US men’s national team captain struggled to get involved in the match in his short few minutes on the pitch. He had a chance in extra time but looped his header miles wide of the goal after a scramble at a free-kick.
Unused subs: Marcus Bettinelli, Edouard Mendy; Trevoh Chalobah; Ruben Loftus-Cheek, Carney Chukwuemeka, Conor Gallagher, Denis Zakaria.