Sven-Goran Eriksson felt his Ivory Coast players had made their country proud despite seeing their World Cup campaign end.
Ivory Coast ran out comfortable 3-0 winners over North Korea in their final Group G game in Nelspruit but it was not enough to earn a place in the second round.
The African side claimed a creditable draw with Portugal in their first match but their chances of progressing from a tough group were ultimately undone by a 3-1 loss to Brazil.
Former England and Mexico boss Eriksson said: "It is a pity we have to leave because this team is getting better with every training session, but that is life - we are out and we have to accept that.
"If you look at the three games we have played, they should be very proud of themselves and the country should be proud of them. The team are leaving the World Cup with their heads held high."
Ivory Coast went into the game with a theoretical chance of progressing but it would have required victories for both them and Brazil, who faced Portugal, with a nine-goal swing in their favour.
That task was rendered irrelevant by the draw in the other match, but Eriksson's side certainly played as if it was possible.
They completely overran a poor North Korea side and bombarded their goal with 28 shots. In the end, they only had goals from Yaya Toure, Romaric and Salomon Kalou to show after a combination of wastefulness, bad luck and belated Korean resistance denied them.
Eriksson said: "It is difficult to go out in a situation knowing you have to score eight goals to go through but they kept their discipline and created a lot of chances."
Eriksson's short-term deal to coach Ivory Coast has now come to an end and speculation about his future has already begun.
The former Manchester City manager has already been linked with a return to England with Fulham - should Roy Hodgson leave - but Eriksson would not comment on his future, other than to say it is not with Ivory Coast.
The Swede said: "It was very clear when I took the job it was to the end of our World Cup and that is today.
"From tomorrow I will stay in some days, maybe watching some football and then I will take some holiday - then we will see. I don't know."
North Korea's decision to switch to a five-man defence in the second half spared the Asian side from embarrassment akin to their 7-0 thrashing by Portugal on Monday.
Ivory Coast fired 10 shots on target in the first half and they briefly entertained thoughts of scoring the required goals.
Coach Kim Jong-hun felt North Korea could look back on their whole tournament, the country's first for 44 years, as a positive experience.
Kim said: "We have participated at the World Cup. We did not manage to attain our goals but we played against Brazil and Portugal, two strong international teams.
"I believe that, though we did not have good results, this has laid the foundation for us to grow in the future. This has been a very useful experience for us and it is a wonderful opportunity for us to grow our football."