Some encouraging practice times had suggested McLaren might be closer to the front at Monza.
Although it got both cars into Q3, with Sergio Perez eighth and Button, the Briton reckons saving tyres for the race would have been a better tactic.
"Obviously it's not what we're here to do, but I think we all realise that now," he said.
"But it's not what the fans come to see, so we did the right thing in a way.
"If we hadn't run, it would have made our options a bit more open in the race tomorrow."
Button said he had not really expected much better from qualifying, as he felt McLaren had shown more of its hand in practice than its rivals had.
"I think we sort of proved how fast the car will go [in practice]," he said.
But he did admit that being three tenths behind the cars in front - with Daniel Ricciardo's Toro Rosso just ahead of the two McLarens - was a concern.
"They have a slightly bigger gap than we thought," said Button. "Three tenths in Q3 is a little bit too much.
"I don't know where we stand in terms of pace in the race, so it's going to be interesting to see where that is.
"I think everyone's going to be on pretty similar strategies so we might have to make it work another way."
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