The 25-year-old high jumper, who was one of three to win Olympic bronze at London 2012, had to make do with second with a leap of 2.29m on his first appearance of 2013.
Russia's Aleksey Dmitrik took the win with an effort of 2.31m to lead his country to victory over America, courtesy of more individual victories, with Britain placing third.
Grabarz's height was spot on the qualifying standard for March's European Indoor Championships with a finish of at least second at the trials now needed to secure his place.
And, with the first part of the job done with his opening appearance of the year, Grabarz insisted he was content with his performance in Glasgow.
"It was my first competition of the year and it was a solid start," said Grabarz – who tried but failed at both 2.31m, twice, and 2.33m once.
"I went for the win and I didn’t pull it off but it was a solid start. I took myself away to Australia after the Olympics and came back refreshed and ready to train.
"And that height was the [European indoor] qualifying mark and now I have to set myself up for that."