The 2009 world champion started 12th on the grid at the Red Bull Ring, and finished just one place higher at the end of the race.
The Briton told Sky Sports News: "I'd hoped we could make up some places today, but it's never easy to overtake around here. We went for a different strategy, starting on Primes, but it didn't really work for us.
"At the start, Nico [Hulkenberg] pushed me wide at the exit of turn one, there was no real need for that as there was enough room for both of us, so I lost a couple of places.
"From then on, my race was all about sitting in the train, waiting for people ahead of me to pit, and trying to make my strategy work, which in the end I couldn't. It was a long afternoon's work for 11th place. I'm now really looking forward to Silverstone."
Button has finished outside the points in four of this season's eight races so far, leaving him eighth in the drivers' standings.