A free-kick by Libyan midfielder Tareq El Taib three minutes before the break secured a 1-0 victory for the Saudi side at Yadegar-e-Emam Stadium, sending Al Hilal through to the knockout stage while denying the Iranian club a place in the last 16.
It was the third straight loss in Group A for Saba Battery, who have been eliminated from the competition after managing only two points from five games.
Karimi was far from happy with the below-par performance of his players.
"Apart from (goalkeeper) Almir Tolja I’m unhappy with my players," said Karimi, who achieved Iran’s last continental club success when he led Pas to the Asian Club Championship in 1993.
"Our players didn’t show their usual quality and played poorly. Even the substitutes didn’t play well."
Karimi admitted that he had rested some of his key players for the upcoming quarter-finals of the Hazfi Cup, the club’s only remaining hope for silverware this season.
But having seen league rivals Sepahan and Esteghlal also fall at the group stage of the Champions League, the Saba Battery boss feels that the heavy schedule has had an adverse effect on the Iranian challenge on the continental stage.
"Sepahan, Esteghlal and ourselves have suffered because of the league pressures. In less than eight months we’ve played 40 matches.
“Even before the match, our focus was on the Hazfi Cup.”
It was Abdullatif Husain’s first match as coach of Al Hilal since taking over from the sacked Georges Leekens and he was naturally delighted with the result.
"As I said before the match, we came here to win and that’s what we’ve achieved," said Husain, who went into the match without the suspended duo of Saudi Arabia international striker Yasser Al Qahtani and Romanian midfielder Mirel Radoi.
"We were missing some key players but the replacements were excellent.
“I want to congratulate all of the players," he added.
Al Hilal will face group leaders Pakhtakor of Uzbekistan in their final Group A game in Riyadh knowing that a win will take them into the last 16 as group winners.