Vickery, a Test Lion in Australia four years ago, accepts that playing for his club Gloucester again must take priority as he recovers from a broken arm.
"Of course it is disappointing not to be involved, but it is a privilege to have gone on a Lions tour back in 2001," he said.
"Realistically, you can't expect to be picked if you haven't been playing. If I am honest, then it is the right call.
"The Lions will need players who are 100% fit, and there are a few in a similar position to me. I have got to get back playing for Gloucester, and that is first and foremost on my mind."
Centre Tindall looks unlikely to play for Bath again this season due to a serious foot injury and seems set to miss out on a chance to challenge the All Blacks.
Fly-half Wilkinson, however, could yet board the plane as Woodward's 45th player.
Wilkinson, England's World Cup final hero, is currently recovering from a second knee injury of the season, but he could return to action for his club Newcastle in Friday night's Zurich Premiership clash at Northampton.
Wilkinson, who has not played international rugby since the World Cup triumph 17 months ago, is running out of time, but such is his potential worth to the Lions that Woodward will undoubtedly wait for as long as possible.
Woodward's squad is made up of 20 Englishmen, 11 Irish, 10 Welsh and just three Scots in scrum-half Chris Cusiter, hooker Gordon Bulloch and back-row forward Simon Taylor.