"As the years go by, each time he gets better and just as important for us on the pitch as he is off it," Busquets told Cadena Ser radio.
"It's marvellous to have him with us, he is magical."
Named Man of the Match against the Czechs, Iniesta received plenty of praise in the Spanish media.
"When he takes two steps, it's two steps forward for the team and two steps back for the rivals," El Pais said in an opinion column.
"With Iniesta everything is possible," wrote online newspaper El Confidential.
A headline in El Mundo said: "Iniesta holds Spain's map."
Iniesta, who made his 110th appearance for Spain on Monday, said he was happy to still be fit enough to make a difference for his national team.
"I said many years ago that I wish I would still be asked the same question in years to come as to if I thought I was still at the top of my form," Iniesta told Cadena Cope radio.
"I celebrate that I'm healthy, that I'm still able to finish the games well, and that is the important thing."
Spain have had the ideal start but have plenty to do to win the tournament for a third straight time. They next meet Turkey in Nice on Friday.
"There is no point in having a good game and then following it with a terrible performance," Iniesta said.
"We have to plan the game against Turkey with the same motivation and enthusiasm as we did against the Czechs."
Turkey lost 1-0 to Croatia in their Group D opener on Monday. Spain end the group stages against Croatia on June 21 in Bordeaux.
(Reporting by Adriana Garcia; Editing by Robin Pomeroy)
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