Kyogo Furuhashi and substitute Daizen Maeda put the visitors 2-0 ahead, with the latter goal coming six minutes from time.
It was almost immediately followed by a reply from the hosts from substitute Ross Tierney, who volleyed in from close range, but Celtic held on to secure an eighth successive domestic win.
Postecoglou admitted the performance had not been one of his side’s best in recent times, but he was happy with the way all his players continue to contribute, often off the bench, amid the hectic schedule.
“It was a bit of a grind tonight,” he admitted. “We never really got into the rhythm we wanted.
“Credit to Motherwell for really working hard. We didn’t start well and complicated things. We made the game difficult for ourselves.
“But it’s not easy away from home so another win is good.
“They worked hard and disrupted us. When we’re playing well, we move the ball quickly and find simple solutions. We tried to be too cute, we didn’t play the obvious pass. We didn’t control the game the way we wanted to.
“We could play better but a big part of this team is their character when we’re not at our best. Winning away from home in the Premiership is never easy. I prefer to play well every game but over the course of a season that’s impossible. They’re human beings.”
A fine clipped goal from Jota in the second half for offside after brilliant work from Kyogo was controversially chalked off for offside after a VAR check, although the Celtic manager was circumspect. “Yeah, I thought it was a good move,” said Postecoglou. “But we had good opportunities to take advantage of the space out there. It just happened too infrequently.”