Spain would not be continental or world champions without record scorer Villa's four goals in Austria and Switzerland four years ago and his five in South Africa two years later, while inspirational defender Puyol contributed a crusading spirit and a wealth of experience that will be sorely missed.
Coach Vicente del Bosque's three strikers - Fernando Torres, Fernando Llorente and Alvaro Negredo - are very different players to Villa, whose pace and guile perhaps made him a better fit with the team's playing style based on swift passing and clever movement.
Torres, whom Del Bosque seems set to include in his starting line-up when Spain begin their Group C campaign against Italy in Gdansk on Sunday, had an indifferent season with Chelsea, while Llorente and Negredo are more impact players who come off the bench to shake things up late in the game.
In central defence, Gerard Pique will likely partner Sergio Ramos but neither commands the same respect in the squad or packs as much of a punch on the pitch as the shaggy-haired Puyol, whose finest moment was the towering header that knocked Germany out in the 2010 World Cup semi-finals.
"It's an absence that is painful for all of us," fullback Alvaro Arbeloa said of Puyol after Spain completed their first training session at their base in Gniewino, Poland on Wednesday.
"He is a player who is always switched on, he is physically very strong and fast and he not only gives a lot of confidence to the defence but also to the forwards," Arbeloa, who trained normally after shaking off a minor neck injury, told a news conference.
"He also has a great deal of experience and his character both on the pitch and off means that obviously we will miss him.
"But others have come in his place and we'll try to make sure he is missed as little as possible."
Javi Martinez, who can play as a defensive midfielder or in Puyol's usual position in central defence, told the same news conference the two absent players had made a vital contribution to Spain's European and world titles.
"But we have other players who have come here who can do the job the same or better and I am sure that with them we won't notice their absence too much," he added.
Injury concern Cesc Fabregas successfully came through Wednesday's session and looks to have recovered fully from a hamstring strain, while Jesus Navas also took part.
The pacy winger had a checkup on Tuesday after sustaining a blow to the hand in training but a scan showed he had not suffered significant bone damage.
After playing Italy, Spain meet Ireland and Croatia and Arbeloa dismissed a suggestion that the heavyweight pair would progress to the knockout round with ease.
"For me Croatia and Ireland are both really good teams with good players and you never know what can happen," the former Liverpool man said.
"I know Ireland very well and physically they are really, really strong and are always fighting," he added. "For Italy and for us it will be difficult."
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