The world number five heads up a team that also includes Nicolas Almagro, ranked 12th in the world, Marcel Granollers and Marc Lopez.
"Ferrer is an example to follow," Corretja told a news conference.
"He said at the end of last year that he needed to rest, but he has reconsidered and when he has been needed, he has said yes."
World number three Nadal said on Monday he needed another two months off the courts to fully recover from a partial tear of the patella tendon and an inflammation of the Hoffa's fat pad in his left knee.
He has not competed since suffering a shock second-round defeat at Wimbledon in June, and has missed the Olympic Games and the U.S. Open.
"I want to thank Rafa Nadal for the effort he made to try and be with us," Corretja added.
"He tried but it wasn't to be, and I would like to pass on his commitment to the team. If he isn't here, it isn't because he did not try."
Spain, who are chasing a fourth title in five years, have the edge in recent encounters against the 32-time winners having won the last two times, though the countries are tied overall with five victories apiece.
John Isner and Sam Querrey will spearhead a new-look USA line-up in the tie.
Isner and Querrey will take on the daunting prospect of filling the two singles berths after the retirement of Andy Roddick and the unavailability of Mardy Fish, who pulled out of the US Open this week because of undisclosed health issues.
"This one is the ultimate ask in current Davis Cup tennis," US captain Jim Courier told a news conference on Tuesday. "Going into Spain, playing them on red clay, they haven't lost in a long, long time.
"We certainly feel like we're going to have a chance, but we also feel like we're not the favourites."
The winner will play either Argentina or Czech Republic, who meet in the other semi, in the final in mid November.
David Nalbandian, Argentina's perennial Davis Cup gladiator, is out of the tie against the Czechs.
Argentina's captain Martin Jaite has named world number eight Juan Martin del Potro, Juan Monaco, Carlos Berlocq and Eduardo Schwank as his team for the September 14-16 tie at Parque Roca on the outskirts of Buenos Aires.
Nalbandian, who has played for Argentina in three finals since 2006, is suffering from a rib injury that put him out of the US Open.
The former world number three, now ranked 45, would probably not have played singles in the tie but would have teamed up with Schwank in the doubles.