Foakes was dropped to accommodate stumper-batsman Bairstow, who scored six centuries in 2022 before suffering a leg injury in September that kept him out of the Twenty20 World Cup in Australia.
In Bairstow's absence, Foakes established himself as first choice behind the stumps under coach Brendon McCullum and captain Ben Stokes during the team's streak of 10 victories in 12 tests.
"I've been in that same position previously around getting dropped so I've got a huge amount of sympathy for Ben (Foakes) and for anyone really who gets dropped," Bairstow, who last kept wicket for England in a test in 2021, told the BBC on Wednesday.
"He'll be back I'm sure because in the last 12 months he's been a big part of what we've been about, he's been a big part of the group.
"It's never an easy decision and never a position you want to be in."
Former captain Michael Atherton supported the England board's decision to pick Bairstow over Foakes.
"My own view is that Bairstow is more likely to help England win a match with bat than lose it with gloves. He would be my choice," Atherton wrote in his column for The Times newspaper.
"It is not hard to imagine the destruction he might cause, coming in at number seven against an old ball and a tiring attack."
England will face Ireland at Lord's on June 1st before the five-test Ashes series against Australia begins at Edgbaston on June 16th.
