The Blues were far from the excellent form which gave them a 2-1 away victory over Al Ahli two weeks ago.
Esteqlal manager Samad Marfavi said the tight schedule of Iran's Premier League, the Hazfi Cup and the AFC Champions League have exhausted the players and resulted in their lack of concentration during the match.
Marfavi was criticized for bringing Esteqlal's top scorer Arash Borhani only in the last few minutes of the match.
However, he defended his decision, saying Borhani had just recovered from an injury and could not play from the beginning.
Later on Tuesday, Qatar's Al Gharafa beat Saudi Arabia's Al Ahli to stand in Group A first place with six points out of two matches. Esteqlal is second with four points.
AFC Champions League Tuesday match results
Group A
Esteqlal (IRI) 0 Al Jazira (UAE) 0
Al Gharafa (QAT) 3 Al Ahli (KSA) 2
Group E
Kawasaki Frontale (JPN) 1 Beijing Guoan (CHN) 3
Melbourne Victory (AUS) 0 Seongnam Ilhwa (KOR) 2
Group F
Changchun Yatai (CHN) 9 Persipura Jayapura (INA) 0
Jeonbuk Motors (KOR) 1 (Eninho 41) Kashima Antlers (JPN) 2
Playing later
Group B
Al Wahda (UAE) vs. Bunyodkor (UZB)
Al Ittihad (KSA) vs. Zobahan (IRI)