Port lost 2-0 to Hong Kong's Kitchee in the Thai League 1 side's debut in the AFC Champions League group stage at Buriram stadium on Thursday night.
In the other Group J match at the same venue in Buri Ram, Japan's Cerezo Osaka defeated Guanghzou FC from China 2-0.
Roberto opened the scoring for Kitchee in the 37th minute and Dejan Damjanovic finished off Port in the 79th minute.
With the strike, Damjanovic is one goal shy of becoming the all-time top scorer in the ACL.
The 39-year-old forward has now scored 37 goals in the Asian club championship, level with retired South Korean striker Lee Dong-Gook.
"Now, I will try to be the first one," the former Montenegro striker said.
"I have five games more, five more chances and I know with my teammates I can do that."
The Thais could have gone 2-0 ahead in the first 10 minutes but John Baggio and Bordin Phala found their efforts hit the woodwork.
All Group J matches are being played at Buriram stadium.
Meanwhile, Thai League 1 champions BG Pathum United should have few problems when they take on the Philippines' Kaya in Group F tonight at 9pm.
In the other Group F game, Vietnamese champions Viettel meet ACL title holders Ulsan Hyundai at 5pm.
All Group F matches are scheduled at BG's Pathum Thani stadium.
BG forward Teerasil Dangda said he was excited to play in the ACL again.
"Everyone at the club, including myself, is excited about the tournament. This is Asia's biggest club competition, so everybody is excited and motivated to do well in the club's debut at this stage," said the Thailand striker.
"It is an advantage to play at home. Still, I believe there is no easy game in this tournament as every team is a top team."