Miller started on the front row in third place after Saturday's wet/dry qualifying at Le Mans and twice managed to pass reigning champion Marquez's Honda in the early laps.
But he faded to fourth behind factory Ducati riders Andrea Dovizioso and Danilo Petrucci at the finish.
"I maybe got a little bit carried away at the start and used a little bit too much of my edge of the tyre," Miller explained.
"I tried to get in front of Marc because I felt I had the speed but I didn't know if I was going to keep the speed for the whole race.
"So I tried to get in front of Marc and slow the pace down a little bit but he was able to get back past me after about two laps and once he got back past he was just able to chip away like a tenth per lap, bang, bang, bang, bang, till it got to about a second and then he was pretty strong.
"It was nice to get the pass on him and to show that we can fight but I just need to understand a little bit more how to do the laptime without using the edge of the tyre like I did."
Jack Miller, Pramac Racing
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