Substitute Juan Carlos Valeron scored the decisive goal in Faro and ensured the Spanish started their European Championship campaign in the perfect manner.
Allied to Portugal's shock defeat to Greece, Spain are now in a strong position to qualify for the quarter finals.
But Real Sociedad midfielder Xabi Alonso, himself a second half substitute, is keen to play down the significance of the victory, particularly with Greece the next opponents.
"We were very concentrated for the match," said Xabi Alonso. "Now it is necessary to be calm.
"Little by little, there are things that we have to improve and to think about for the next match.
"We know that we cannot take a result against Greece for granted. Greece played a very serious match and they deservedly took the points."
Valencia midfielder Albelda echoed his international team-mate's sentiments about Spain's desire to start with a win and revelled in main rival Portugal's defeat.
Albelda commented: "It was important to begin with a victory. It is possible to play better or worse but the most important thing is to win, particularly after Greece's victory.
"Portugal's defeat is good for us. Everyone thought ourselves and Portugal would qualify easily and now we have seen that things are not so easy,"
