The European champions, whose style has become known as "tiki-taka" after the speedy, one-touch football they typically deploy, were shut out by the battling Swiss in Wednesday's shock 1-0 defeat in their Group H opener.
Midfielder Alonso and defender Pique told a news conference at Spain's training base on Friday the team's style was clearly-defined, had served them well in the past and it would be wrong to make drastic changes because of one poor result.
"The other day (against Switzerland) we played well but we failed with the final ball, but we are not going to change our style," Pique said.
Alonso added: "The system has worked well in other matches, allowing responsibilities to be effectively shared out. It's possible we'll find ourselves in a similar position (to the Swiss game) again and we'll just have to break down our opponents as best we can."
Coach Vicente del Bosque fielded a cautious 4-5-1 formation against Switzerland and was criticised by his predecessor, Luis Aragones, for not placing more emphasis on all-out attack from the start.
Only after Spain went a goal behind early in the second half did Del Bosque throw on striker Fernando Torres to join David Villa up front, also introducing wingers Pedro and Jesus Navas.
"Our style is defined but that's not to say that we don't have other options," Alonso said.
"Our opponents know us but we have the weapons to solve problems against teams that sit back."
One option Del Bosque did not use against the Swiss was midfielder Cesc Fabregas, who is kept out of the side by the embarrassment of riches in the Spanish midfield, including Xavi, Andres Iniesta and David Silva.
Del Bosque also has hulking striker Fernando Llorente in reserve, whose strength and height might be the key to unlocking unyielding defences.
"Cesc has great touch and timing and can also score goals," Pique said. "He's in great shape and clearly if the coach selects him he'll bring a great deal to the team."
Spain play Honduras in their second match of the World Cup on Monday in Johannesburg and their third and final game of the group phase is against Chile in Pretoria on June 25.
