The Liverpool 'keeper feels La Roja were unlucky to suffer a 1-0 reversal against Ottmar Hitzfeld's men and is confident they will turn their fortunes around beginning with their clash versus Honduras on Monday night.
"It's obviously a setback," said Reina. "We're obviously really disappointed, but we have two games ahead and if we win them I think we'll go through.
"So now we have to focus on getting ourselves ready for the next game. We knew that any opponent here was going to be tough, and maybe this was good for us to lose now, so we pay a bit more attention and wake up a little bit for the future games.
"I think one thing is clear - we didn't deserve to lose. Unfortunately we did. But the team played good football, we made a lot of chances and it was just one of those games. It was more or less like the game we played a year ago against the USA in the Confederations Cup. We have to react and win the next two games."
Spain arrived in South Africa as overwhelming favourites to secure the title but Reina insists they must learn to cope with the pressure of expectation if they are to become the first team to land the title after losing their first game.
"We've never felt ourselves to be favourites at all," said Reina. "That was something that was said by other people, which is something we can't control. But of course, we have to handle that pressure.
"We don't consider ourselves clear favourites, because there are so many strong and powerful teams here, like Brazil, Argentina, Germany, France, Italy and many others. We've never done particularly well in the World Cup as a nation, but I don't think there's extra pressure on us because of that. We want to win the World Cup and we will try to do that.
"It's an open tournament, but it's tight at the same time. Almost every game so far has been tight, with not many chances. Football is like that these days, and it's never easy to win when a team is defending well like Switzerland did. It's difficult to break them down."
Despite notching up 22 shots on target, Spain still failed to find the net against the Swiss. Reina concedes it was a frustrating game to watch but feels his teammates must remain loyal to the style that has seen them lose just twice in 46 matches.
"Now is the time for us to recover, stay fit and get ready for the next game," said Reina.
"We must be loyal to our philosophy and believe in ourselves more than ever. We are still depending on ourselves, and that's a positive position to be in. But we have two must-win games coming up and we have to do that. It's in our hands."
On a positive note, the clash with the Swiss saw Fernando Torres emerge from the bench to make his first appearance since undergoing knee surgery two months ago.
Reina believes his Liverpool teammate will still play an important role for Spain and has backed him to make a key contribution in the latter stages of the competition.
"Fernando is an important player for us," added Reina.
"It's always been like that and we cannot expect anything less than the best from him, so let's see if he can score in our next game.
"I don't know if he's 100 per cent fit. After two months out it's always difficult to come back and be 100 per cent straight away, but I am sure he will be later on at this World Cup."