The 3-1 home defeat extended the team's winless run to eight matches - seven in the Bundesliga - and places huge question marks over 49-year-old McClaren's ability to sweet talk the directors into keeping him after the winter break.
McClaren, who had an unhappy spell in charge of England leaving the post when they failed to qualify for Euro 2008, has only been in the hot seat since July after rebuilding his career at unfashionable Dutch outfit Twente, whom he guided to the 2010 domestic title.
However, Wolfsburg general manager Dieter Hoeneß refused to be rushed into a decision.
"It is imperative we don't make a hasty decision," said Hoeneß. "We must first of all digest this failure. But we do not have a plan B."
McClaren for his part admitted that there were deep seated problems at the club, who were crowned champions in 2009.
"I am angry and frustrated," said the former Middlesbrough manager, who was best known for being an admirable assistant to Sir Alex Ferguson at Manchester United.
"We have problems in the dressing room, and on the pitch. This club needs changes to be made.
"Which ones? I don't know, it is not for me to judge, no-one knows what will happen in the days to come, but it is imperative that a clear signal is sent."