The Spaniard was dismissed for two bookable offences as Arsenal edged into the last 16 of the Champions League in second place.
Jenkinson thinks Arteta would not have been shown a second yellow card had it been a Premier League game.
In the second half I don't feel we really played our football and that invited the pressure onto usCarl Jenkinson
"I think in the Premier League he wouldn't have got sent off but sometimes it can be like that in European football," Jenkinson told Arsenal Player. "Mikel [Arteta] has made two fouls the whole game and he somehow managed to get sent off.
"I think the first one was a booking in all honesty but the second one was incredibly harsh. I don't think their lad has done him many favours with his reaction and then he's got straight back up which is never nice to see."
Despite sealing qualification for the knockout stages for the 14th consecutive season, Jenkinson was disappointed with the team's performance in Naples.
"It was a really difficult night," he said. "To be fair to them [Napoli], they were very good and they pressed us from early on.
"We came here to win the game, of course we can't be stupid and go gung-ho because if you concede a goal in a game like this early on you make it difficult for yourselves.
"I thought going into half-time we were very comfortable and then in the second half I don't feel we really played our football and that invited the pressure onto us."Copyright 2016 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source