The Manchester City forward said the European champions were not much better than Paraguay in their hard-fought 1-0 win at Ellis Park on Saturday.
It took David Villa's fifth goal of the tournament seven minutes from time to secure passage into the last four for the Spaniards, but Santa Cruz expects the going will get even tougher for them against Germany.
"I think we needed a little more luck and we showed that we could have won," said Santa Cruz, who had a couple of late chances when he came on as substitute, one which look sured to produce an equaliser before Iker Casillas made a fine parry.
"Spain weren't better than us, anything but, and we had our chances during the course of the game.
It was a far from convincing performance from Spain, who made history by reaching the World Cup semi-finals for the first time after finishing fourth in the 1950 tournament when there was no semi-final format.
Both goalkeepers saved second-half penalties before Villa's late intervention ended Paraguay's quest to reach the semi-finals for the first time.
"We've got the team to keep on progressing but we have to accept our fate," Santa Cruz added. "We are very disappointed and it was frustrating to lose. We thought we played a great game and things didn't work out at the end.
"We are very proud to finish with that kind of performance we showed against Spain."