Back was cited for punching Joe Worsley in the Zurich Grand Final and was suspended on Thursday night until June 14 by a Rugby Football Union disciplinary panel.
Lions head coach Sir Clive Woodward believes Back has grounds for an appeal but feels it is best to accept the panel's verdict.
Woodward said: "I do believe Neil has grounds to appeal. But at this stage of our planning for the tour, it seems advisable that we move on and focus on the challenge ahead."
Back said: "I was surprised to get a four-week ban but I have decided that there is no point appealing against it.
"An appeal hearing would have taken place on Monday, when the Lions play their first game of the tour against Argentina.
"I think it is better for everyone that we now focus all our minds on the massive challenge ahead. That is what I intend to do."
Back was in line to play against Argentina but fell out of consideration after being cited for the punch that left Worsley, his former England team-mate, with 13 stitches in his mouth.
Back will also miss the Lions' tour opener against Bay of Plenty on June 4, the clash with Taranaki four days later and the first big test of the tour, against the New Zealand Maori on June 11.
He is almost certain to play against Wellington on June 15 and Woodward insisted that he will still play a central role in the tour.
"Everyone involved in the Lions tour of New Zealand recognises the very special qualities Neil Back brings to the game and he will have a crucial role to play on the tour," said Woodward.