Anelka has been selected in France's provisional 30-man squad for next month's tournament, but the party must be trimmed to 23 by Wednesday.
The France coach feels sympathy for the forward, but could leave Anelka out of his European Championship plans, if he believes the spot-kick miss has affected the 29-year-old.
"It is something I have to think hard about," Domenech told reporters at France's training headquarters at Clairefontaine.
"We'll also have to see how the other players speak about it. If they wind him up, how will he react? It's difficult to say.
"It's embarrassing for the person who misses. Furthermore, he is France and part of the French team.
"I certainly felt for him. Nicolas was put in the position where he had to save the team because Ryan Giggs had scored his penalty."