An early Jonatan Germano goal was the difference between the two teams at AAMI Park, the result sending John van 't Schip's men eight points clear in sixth place, with five matches remaining for the reigning champions, who are seventh.
The Roar's interim coach acknowledged the fact the odds are now stacked against his team, but insisted they will continue to fight until it's mathematically impossible for them to finish in the playoff places.
"It's a lot more difficult now," he said.
"Not so many games to go. It's still possible of course, we'll still go for it. As long as it's possible, you have to go for it."
Thijssen defended his decision not to make a substitution in Melbourne, claiming he left striker Andrija Kaluderovic on the bench because he had confidence the players on the field would find a way past the City backline.
"I thought we were so much on top, creating chances," he said.
"In the end we didn't get a goal. I was still hoping for a goal. We were the better team and got into the penalty area a lot.
"I think we deserved more than this, even in the first half I thought we were the better team and creating more chances. In the second half we were really on top."
The Dutchman praised the performance of Jade North, who - having only been named in the squad at late notice after recovering from a groin problem - was thrust into the starting XI when Jerome Polenz injured his quad during the warm-up.
"It was a big risk for us to start with Jade North. He plays 90 minutes without any training in the last weeks. He did a great job, you see his experience and quality. He did a great job."