The Barcelona midfielder is desperate to do well at the European Championships, and has stressed that his relationship with Real Madrid's Iker Casillas remains excellent
Both players formed an important part of the Spain squad which won the 2010 World Cup but have missed this summer's tournament due to injury.
However, Xavi is hopeful of bringing the injured pair happiness with victory in Poland and Ukraine.
"Puyi is a leader, a winner. And Villa is our historic goalscorer. But they are not here. We'll try and give them some joy," Xavi stated to TVE.
"They are two champions, but injuries are part of football, too. Their replacements are giving their all for the team."
The influential midfielder also insisted he enjoys a good relationship with Real Madrid goalkeeper Iker Casillas, despite rumours of tensions between players from the 'Clasico' sides.
"Casillas and I get on stupendously. We have been friends since we were kids and nothing is going to break that," he added.
A 2-2 draw against Croatia in their final group game would ensure that both sides qualify for the next round at the expense of Italy, however, Xavi has denied that the teams would collude.
"There's no way that there will be a pact. We want to attack and playing for a tie doesn't fit our style. The game against Croatia is not different. We will go out for the three points," he continued.
Monday's encounter in Gdansk kicks off at 20:45CET.