Paraguay succumbed to a 1-0 defeat to Spain in the quarter-finals after Oscar Cardozo had seen his penalty saved by Iker Casillas, but can be satisfied with a tournament that saw them top Group F and beat Japan in the second round.
The squad arrived back in Asuncion on Monday and Martino confirmed that with his four-year contract expiring, he will not be extending his spell in charge of the national side. However, he will help in a period of transition as his replacement is found.
Santa Cruz, who made his international debut in 1999, has scored 21 goals in 80 appearances for Paraguay but will not be a part of the country's plans for the 2014 World Cup.
The Manchester City striker has struggled with injury problems throughout his career and is aiming to ease the strain on his body. He may take part in the 2011 Copa America.