Arshavin, 28, and his Russian teammates dazzled at Euro 2008 for a place in the semi-finals, but were caught out cold by Slovenia in a World Cup play-off tie.
"I cannot say that this is the deciding moment in my career - only after years will people usually realise it. But, in any case, to stay out of the World Cup means to be on the sidelines of world football for a time," Arshavin was quoted as saying when elimination was already looming after the first game in Moscow.
As a result, the Arsenal forward Arshavin will not be in South Africa, and neither will Barcelona striker Ibrahimovic, whose Sweden team were eliminated as well.
The exit prompted Ibrahimovic, 28, one of the world's best paid footballers, to reconsider his national team future.
Given his age of 32, Ukraine's Shavchenko will most likely never appear on the global stage again as the next World Cup is not until 2014.
The former AC Milan and Chelsea forward only managed to qualify for one big event, the 2006 World Cup, as Ukraine went out for the fourth time in a big event play-off series.
The Ukrainian defeat against Greece also means that none of the Euro 2012 hosts will be playing in South Africa as Poland missed out in the group stage.
Also missing from the showpiece of international football are African champions Egypt, who were beaten in a play-off by north African rivals Algeria after they both finished their group equal on points, goals scored and conceded.
2002 World Cup semi-finalists Turkey and Croatia, who managed the same feat in 1998 will also not be in South Africa.
The history of the World Cup is full of prominent players and teams which have failed to qualify.
The best-known players are George Best, who starred for Manchester United but failed to lift Northern Ireland to a big event and George Weah, who won just about everything in an illustrious club career, but had the bad luck of being born in Liberia.
Big teams like England and Italy have missed out in the past as well, and so did the Dutch who were the most prominent no-show at the 2002 World Cup.
This time around the Dutch were the first European team to qualify, while World Footballer Cristiano Ronaldo had to sweat until the end before his Portugal side beat Bosnia-Herzegovina in the playoffs.
The possible 2009 World Player Lionel Messi was also given a fright before his Argentina team squeezed through.