Spanish coach admits concern over shorter break to prepare for Portugal semi-final clash as his side keep France under control.
Euro 2012: Spain's defenders could hold key to retaining title, says del Bosque
Alonso, winning his 100th cap, put the defending champions in front with a fine header from Jordi Alba's cross after 19 minutes.
The midfielder then made the game safe in stoppage time from the penalty spot after Laurent Koscielny had upended Pedro Rodriguez inside the area.
Despite not hitting their top form, Del Bosque was delighted with how his side restricted the French to just one shot on target
"The truth is we did well and controlled the game," said Del Bosque. "Iker (Casillas) hardly had anything to do and that speaks of the good defensive performance of the team.
"If our defenders are good then we will be closer to winning the tournament because we will always create a chance."
The former Real Madrid boss was particularly pleased with Alonso's determination to make the run into the box that resulted in the first goal, and reiterated his belief that both he and Sergio Busquets offer important options going forward.
"Alonso is one of the players that has scored most in my time as manager," said the coach.
"I already know that he and Busquets are a controversial pairing but I always defend that these are more attacking footballers than defensive ones.
"They have an extraordinary awareness of the team."
Del Bosque voiced concerns about having less time off than Portugal ahead of Wednesday's semi-final, though, and hinted he could be forced to freshen his side up if the heat in Donetsk is as severe as it was this evening.
"We have two less days to rest than them and I am thinking about this," he said.
"It is a small handicap. We have arrived very drained because the heat we suffered tonight was cruel on the players."
Alonso himself was delighted to mark his century of caps with two goals, but was just as satisfied with how Spain controlled the game throughout.
"We are very happy because we knew it was a game where we had to slog and we have done that," he said.
"We had control of the game from start to finish despite having only a few chances.
"Personally I had satisfaction for the game we have played and to have scored two goals, but the most important thing is that we are in the semi-finals."
The former Liverpool man believes it is more important for the Spanish to concentrate on their own performance in the semi-finals than worry about the threat posed by his Madrid teammate Cristiano Ronaldo.
"At this stage all the games are difficult and we know Cristiano perfectly," said Alonso.
"We have to concentrate on ourselves and try to make a game like today or even better."
France coach Laurent Blanc felt his side would have had a chance if they could have kept Spain out until half-time.
"We had planned some things tonight and we have shown great solidarity. What I regret is that they scored on their first real opportunity," Blanc said.
"The first (attempt) was good, unfortunately for us. I think if we end the first half at 0-0, what was planned, it would have allowed our team to have a bit more morale for the second period.
"I think the boys gave their all. Against Spain, it's hard."
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