Sevilla, who are 13th, had Coke sent off in the 74th minute in San Sebastian.
Carlos Vela fired Basque club Sociedad ahead in the 18th minute before Gary Medel levelled for the Andalusians four minutes into the second half.
Alberto De La Bella restored the home side's lead in the 69th minute and defender Coke then picked up two yellow cards in quick succession and was dismissed five minutes later.
Michel was appointed in February to replace the sacked Marcelino and Sevilla, the 2006 and 2007 UEFA Cup winners, ended the season in ninth and failed to qualify for Europe.
In the earlier kick-off, Levante missed a chance to climb above Malaga and Real Betis into fourth when long-range efforts from Nacho and captain Piti and Franco Vazquez's late strike gave Rayo Vallecano a 3-0 home win.
Levante stay sixth on 27 points, two ahead of Sociedad in seventh and Rayo in eighth.
Real Sociedad controlled possession for about half the match thanks to strong open field play.
Real Sociedad won 53 duels and 14 headers, which led to eight shots, including four on target.
Diego Ifrán had three shots for Real Sociedad, more than any of his team-mates.
Xabi Prieto's 19 passes to Vela were the most of any Real Sociedad team-mates during the match.
Los Nervionenses had 48.5% of the possession during the loss.
Sevilla had 14 shots, including four on target.
The four attempts by Álvaro Negredo were the most of any Sevilla player.
The combination of Geoffrey Kondogbia to Gary Medel was the most common during the match, as the two players connected 14 times.