The McLaren driver and team-mate Sergio Perez had come through to sixth and seventh places as others pitted during the safety car for Sebastian Vettel's stranded car.
But Button said the combination of a late restart and cars behind on newer tyres was a worst-case scenario for McLaren's current issues.
"When the safety car came out at the end, I had quite old tyres and was just a sitting duck," he said.
"I couldn't get any tyre temperature. That's one of our issues anyway and when you've got no tread you definitely can't get tyre temperature.
"I was just waiting for people to pass me. It was tough."
Button was also confused by the McLaren's tyre behaviour earlier in the race, when he struggled with graining on the harder Pirellis then found the softer medium option far better.
"The first stint we went for the primes because nobody else in front was on them, but that was actually the one that grained - front and rear - for me so we had big problems in the first stint," he said.
"We just had to wait until a lap we could pit and put the other tyre on.
"I was much happier on that tyre - strong pace and no graining... work that one out..."
- Sergio Perez
- Sebastian Vettel