The victory gave Poland their only points in the tournament and Engel reflected that his team's fighting spirit took too long to come to the fore.
The coach also revealed that two of his players are set to resign from international football but that he would "let them announce it by themselves".
"The boys didn't understand what it took to be in the world championship until it was too late," Engel reflected.
We lost the first game and it decided about everything
"But today we wanted to show we belong to the world family of soccer. To win was good for us psychologically, we understand now that we can win.
"It's been a group of surprises and it will be very good experience for the qualification games for Euro 2004.
"Poland are in the 16 teams going home but I wish South Korea all the best because of the organisation of the tournament - the people are fantastic."
Engel changed his team but dismissed claims that Poland won because of the five players he drafted in.
"We played well at last, used excellent tactics and were very disciplined.
"I have always put the best on the pitch - I trust the best - and the players were in good shape.
It's a pity we're leaving - it didn't have to be that way
"The defeats were the result of individual mistakes made by the players who up until now were the most important to the team.
"The players that were out today avoided those mistakes - that's the only difference."
Jerzy Dudek was one of the players to miss out as Engel put his faith in players from Poland's domestic league as opposed to those who had carried the country through qualifying.
"Jurek [Dudek] didn't play because I know how a goalkeeper can feel after seeing the ball in his net six times," Engel explained.
Poland's stand-in goalkeeper Radaslaw Majdan was delighted with the result and by the manner in which it was achieved.
"We wanted to make up for the bad start and go out with a win. We played excellent soccer," he said.
Back in Poland, news of the team's success gave Economy Minister Jacek Piechota respite from angry ship workers.
Piechota had been pelted with rotten eggs after announcing the loss of 3,000 jobs and hard to take cover in the Szczecin shipyard's office.
On his return he informed the crowd that Poland had scored two early goals against the United States and chants of "traitor" gave way to cheers.