After starting on pole position, Button retired when he hit the 'Wall of Champions' at the final turn with 23 laps remaining.
"It has been a disappointing end to what has been a very encouraging weekend," he said.
"When I got to the chicane, I had big understeer and hit the wall off the second kerb. It was completely my mistake and very frustrating because we were looking good.
"We were not on the same pace as the leaders but it was looking good for a podium finish."
BAR were championship runners-up to Ferrari last year but this year has been worse than they could have imagined.
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An appeal court then suspended them for two races.
Brazilian Gil de Ferran, the Indy 500 winner now acting as BAR's sporting director, said the team could still take heart from Montreal.
"The overwhelming feeling as we leave Canada and head to the U.S. is a very positive one," he said. "Overall our performance was much improved from the last race and we were challenging at the front end of the field throughout the weekend.
"Hopefully, that's where we'll be in Indianapolis."
The U.S. Grand Prix, ninth round of the 19 race championship, follows next weekend.