The Lotus driver qualified fourth, over three tenths of a second off fastest man Sebastian Vettel but he was only 0.111s off the Mercedes driver.
While conditions meant that the track was slower during his second run in Q3 than his first, during which his fastest lap was set, Grosjean was set to improve until Turn 10 on his final lap.
"I tried [to improve] in the last attempt in Q3," he said .
"I was up by one tenth and then had a bit of rear-locking into Turn 10 and lost that tenth.
"I tried to recover in the last few corners, but the lap time was more or less similar and the track wasn't as quick as the first run in Q2 on the second run, so we didn't manage a better lap time.
"It was more or less where we wanted to be, on the first two runs.
"Red Bull and Vettel and too quick, but we know we could fight with Mercedes.
"I was thinking more of fighting with Ferrari to start with but we were quicker, so that's good."
Grosjean expects to fight for a podium finish in Sunday's race but believes trying to fight Vettel for victory could prove counter-productive.
"You don't start the race not thinking about doing the best, but basically if he flies like was the case in Singapore, it's not worth trying to follow him.
"It could cost you pace [over a stint]. We will see how the degradation is and see what I can achieve in the race and it would be nice to be on the podium."
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