The Barcelona full-back was in disbelief when told by his coach that he would shine in the tournament, while the 61-year-old also discussed his use of the 'false nine' system
The former Valencia defender played a key role in his nation's successful defence of their continental crown - scoring the second goal in La Roja's 4-0 final win over Italy - and won a move to Barcelona shortly after.
And while Del Bosque was never in doubt of the 23-year-old's ability, the player was uncomfortable with the praise being lavished upon him by his coach.
"I told Alba that he would be the best full-back at the Euros, and he looked at me as if to say: 'What are you talking about?'" he said in an interview with Punto Pelota.
The former Real Madrid coach went on to speak about the supposed rivalry between the Blancos and Barca players inside the national squad, and insisted that everybody is united.
"In our midfield we have many Barca boys. There is no division between Barcelona and Madrid. This is Spain."
La Roja played much of the tournament using the 'false nine' system, with Cesc Fabregas playing as the focal point of the attack but dropping deep to create space behind him, due in part to David Villa's absence due to a broken leg.
However, Del Bosque does not believe he would have steered clear of the tactic, even if the 30-year-old was available for selection.
"Villa is used to playing on the left, rather than in the centre. In the tournament, it depended on the match, on whether we wanted a reference point up front, or a man who links up better, like Fabregas."
The 61-year-old also praised Jose Mourinho's coaching abilities, but conceded that he saw himself as a very different person to the current Madrid coach.
"I like him as a coach, but I don't see myself in his role. And I imagine he doesn't see himself in mine."