The Gunners went ahead after only three minutes, after Alex Iwobi’s low cross evaded everyone before finding the bottom corner.
But Sokratis was shown a second yellow, for pulling down Ismaïla Sarr who was through on goal.
From the resulting free-kick, Benjamin Bourigeaud made it 1-1.
Nacho Monreal diverted Mehdi Zeffane’s cross beyond Petr Cech, before Sarr added a third for the hosts on the break.
Speaking to BT Sport, Emery said: “We controlled the first 40 minutes and scored and this is the first target but after the red card we cannot control it.
“When we were 2-1 down it is difficult to have a better result. We wanted to hold the result but Rennes won the first 90 minutes.”
“Now, we have another 90 minutes at home in front of our supporters and we want to be positive, it will be 11 v 11 again.”