"Obviously I had chances in the first set", said the 21-year-old world number five.
Djokovic, who beat Isner in his opening group-stage match, has enjoyed a remarkable renaissance in the second half of 2018 and lifting the trophy on the banks of the River Thames would be the ideal way to finish his year.
Cilic had a 7-3 advantage over the 33-year-old American, but Isner had won three of their last four matches.
Zverev, who won his opening group game against Marin Cilic, now needs to beat John Isner to guarantee qualification for the semis but Antic is expecting big things regardless of what happens this week.
It was highly competitive with Zverev more than holding his own, and even threatening to break the World No. 1, but his failure to do so belied a worse fate, as he double-faulted away the set for Djokovic to take the lead.
Several leading players, including Djokovic, have questioned the timing of the ITF's flagship event, coming at the end of a gruelling 11-month season and Germany's Alexander Zverev said this week he would not play in the showpiece finals.
Zverev was able to keep Djokovic at bay with his thunderous serve at the start of the first set.
My model has the Croat at [1.62], with Isner back at [2.61], which is pretty much in line with market pricing in what I anticipate to be quite a serve-orientated encounter, with both players having projected hold percentages around the 90% mark, with Cilic up at around 95%, bearing in mind Isner's obvious issues on return. I'm looking forward to that match.
"Zverev is obviously the leader of that next generation".
"I think I'll take it as a normal quarter-final match at a normal tournament", said the German, who beat Cilic in his opening match on Monday.
"I thought I played well from midway through the second set, I started to swing through the ball but I haven't served that great".
"A win is a win", the world No. 1, bidding for a record-equalling sixth title at the ATP's blue-riband event, told reporters.
There was one more factor that could play a significant part in his meeting with Isner.
"You have to give him credit for that, for qualifying for World Tour Finals two years in a row".
"Unfortunately, today hasn't been great in terms of that (illness)", Djokovic said.
Djokovic saved the first with heavy serve but then double-faulted, offering Zverev another glimpse. Not just an Isner win will carry the Serb to the semi-finals but a Cilic win in three sets would do the same. Well, she decided she doesn't want to compete at tennis, I wish her really all the best in any future endeavors that she has in her life.