Hodgson's men, who top Group E in qualifying with maximum points from three games, host Slovenia on November 15, less than a week after the Dallas Cowboys and Jacksonville Jaguars do battle in London on Sunday.
The 67-year-old said he felt the surface was already below standard acceptable for international football, and said he was seeking a solution - despite Wembley officials announcing another three NFL matches will be played at the venue in 2015.
"I am a football coach, a football manager, and I am talking about English football, not American football," Hodgson said.
"I don't really think you could expect me to say: 'Excellent, delighted, well done'. I'm realistic, I'm pragmatic and this match [on Sunday] has been organised for a period of time. The pitch, unfortunately, is not in the best of nick anyway, which we're all a bit unhappy with.
"Adrian Bevington [Club England managing director] is in charge of taking this matter forward and I am sure we will find a good solution but at this particular moment in time I would honestly have to say, if I'm asked if it is a good thing or not, I would have to say not.
"I can do nothing about it and we won't use it as an excuse. We will adapt and get on with it and hopefully in the future the pitch will recover to its normal level and when it has done that we will be better able to support this type of activity."
England's final home Group E qualifier is set for October 9 against Estonia, which will be preceded by an NFL game between the Miami Dolphins and New York Jets eight days earlier.
