The trouble, which erupted after Cesc Fabregas netted Spain's winner in a 3-2 success in St. Gallen, Switzerland, coincided with FIFA's Fair Play Day. The world governing body's president Sepp Blatter had said he wanted international matches to set a good example.
"The spectacle we made of ourselves at the end of the game was not gratifying," Del Bosque said ahead of Spain's Euro 2012 qualifier at home to Liechtenstein on Tuesday.
"I understand the anger and frustration of the Chilean team, although I am also aware that we share some of the blame," the former Real Madrid player and coach told a news conference.
The Spanish players said the way they stood up for each other during the fight proved they were united and had buried any suspicions of a rift between the Real Madrid and Barcelona members of the squad following recent acrimonious clashes between the clubs.
Spain, the defending champions, can join Germany in qualifying for the Euro 2012 tournament jointly hosted by Ukraine and Poland with a win over Group I minnows Liechtenstein in Logrono on Tuesday.
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