Walcott was on the bench at Gothenburg's Gamla Ullevi but came on after an hour and set up James Milner's goal in the 2-0 win against the highly-rated Spanish.
Pearce made 52 appearances for Newcastle between 1997/9, scoring one goal.
Pearce: "He just said congratulations, just watched the game and he's pleased as punch with the result, and obviously I'll feed that back to the players.
Former Toon Star Leads 'Brilliant' England To Glory!
"They're the eyes of the man they want on them. Yes, me as their manager, but they want Mr Capello's eyes on them and see that gutsy performance.
"Credit to them and a lot of our players will have done themselves a lot of credit and that's what this tournament is all about.
"I've only ever treated everyone equally.
"People get in and out of the team on merit and that has happened this time.
"I didn't speak to him before, the team went on the board and Theo took it like any member of the staff would take it. He was disappointed but when he came on he put a performance on, going forward and helping by tracking back."
England went into the break goalless after Milner had a penalty saved. Walcott came on after 62 minutes and Fraizer Campbell opened the scoring shortly after, with Milner sealing the victory by thumping home Walcott's cross.
Milner received a yellow card that rules him out of the game against Germany next week, although England will be in the semi-finals even if they lose.