"I was gobsmacked and they wanted a speech, but I couldn't give them anything, bar 'let's go and beat the Germans'.
But he added: "I'll leave any celebrating until I get back to Dublin."
Niall Quinn, the squad's oldest player at 35, said the gesture "epitomized the whole spirit of the squad".
Coach Mick McCarthy was impressed by the performance of central defensive duo Staunton and Gary Breen.
The pair were criticised for their performance in the first-half of the opening match against Cameroon.
"I was critical of the two at the back on Saturday in the first half but in the second they nailed it down and against Germany they were terrific," McCarthy said.
"It was their idea, they went and presented him with a
beautiful watch.
"It's a lovely touch and it showed the feeling they have for one another."