The Republic were comprehensively dumped out of the group stages at last month's tournament following defeats to Croatia, Italy and Spain, with Given's performances subject to some criticism. Goalkeeper Given and centre-back Dunne currently remain on holiday and are not due to return to training with the rest of the Villa squad until next week.
Lambert has confirmed speaking with both players during the Republic's campaign, and will do so again upon their return, but does not anticipate any hangover. He told the club's website: "They're two experienced lads, they're not kids and they've been round the course before."
He added: "Shay has about 955 caps and Richard has a lot too. They know the game, know the high level of football it is, which is great.
"It was a great honour for them, I'm pretty sure, to have taken part in a major tournament.
"Okay, it might not have gone the way they wanted it to go, but they were still part of it, a great tournament. I am pretty sure the experience will be good.
"It was a hard tournament for them with what happened. But they've done great for Villa in the past and had fantastic football careers."