The reigning European champions lost their first qualifier in eight years on Thursday as a late Miroslav Stoch goal condemned Vicente del Bosque's side to a 2-1 defeat in Zilina.
It means Spain have won just once in three matches since their below-par showing at the World Cup in Brazil, with an Iker Casillas error allowing the hosts to take the lead through Juraj Kucka.
While Paco Alcacer levelled with eight minutes to go, Stoch headed in late on to end Spain's run of 36 qualifiers without defeat.
Luxembourg were beaten 3-2 by Macedonia on Thursday, despite leading at the break, and Spain will be eager to avoid back-to-back defeats and falling further off the pace in Group C.
Barcelona midfielder Iniesta has called for patience following the defeat and says his team-mates are focused on a return to winning ways.
"I don't think we need to renounce what he have always done," Iniesta is quoted by AS.
"The only thing is you have to try and get the results to go with the performance, otherwise the feeling doesn't change.
"If you lose, then doubts arise but we're up for it, to reverse the situation. We lost but it's a long road and we have another game on Sunday."
The nations have not met since a friendly in June 2000, where an early Gaizka Mendieta goal settled things in Luxembourg.
Current coach Luc Holtz played in that game, with his side having won only once in their last six competitive home games.
Luxembourg go into Sunday's fixture off the back off a dramatic late defeat to Macedonia but despite Beshart Abdurahimi's late winner in Skopje Holtz is eager to take the positives from the defeat.
"Late in the game, it could have gone in one direction or the other, it was a solo effort that made the difference," he told L'essential.
"But for us to score two goals, it is very positive.
"We must not dwell on this defeat and by Friday we'll focus on Sunday's game against Spain."
In what would be a big boost for Sunday's hosts, Aurelien Joachim could return from a thigh problem while Del Bosque has no fresh injury concerns.
