The 63-year-old believes the Barcelona midfielder was more important to the national side than the coach
The 34-year-old won back-to-back European Championships with Spain in 2008 and 2012, as well as the World Cup in 2010, and was considered the heartbeat of the most successful international team in history.
"I would like to show my recognition to a fantastic player," Spain boss Del Bosque stated. "We have lost a unique player in the national team and it will be difficult to find another one like him."
The former Real Madrid boss added that La Roja had lost the key component in the Tika Taka style that Xavi had played such an integral role in developing at Barcelona and then adapting for the national team.
"Xavi has been key in Spain's style and in all the success achieved," Del Bosque acknowledged. "We'll miss him so much on and off the pitch."
Xavi made 70 of his 113 Spain appearances under Del Bosque and he feels the midfielder should also be remembered for the class and leadership he showed off the field.
"He has given us great support in the dressing room over the last six years," the 63-year-old added.
"He's a player for whom we have so much personal affection - but also affection in terms of football.
"We all agree that Xavi is so important for us - even more important than the coach. He'll always be appreciated by the [Spanish Football] Federation, by the coach and by the national team."