Simeone handed Vietto his senior debut when the pair were at Argentine outfit Racing Club, but the forward came back to haunt his former coach at the Vicente Calderon.
The pair embraced before the start of the game in the capital, but it was Vietto who had the last laugh.
With six minutes remaining in Sunday's La Liga clash, Vietto beat Diego Godin and slotted a calm finish beyond Miguel Angel Moya as Villarreal triumphed 1-0 - Atletico's first home league defeat since May 2013, ending an unbeaten sequence of 27 games.
"They won the game doing a really good counterattack with Vietto. I am so happy for him, but we lost an important game after a year without defeats at home," Simeone said.
"But I am so happy for him because he always showed a lot of skills and could do it.
"I think we lost the control of the game making some mistakes during the last 20 minutes just thinking about the victory.
"To be honest, they made a really good counter-attack to get the goal, a nice goal from a team which worked really well.
"So, we just say congratulations to them and we have to be ready for Thursday [against L'Hospitalet in the Copa del Rey]."
Vietto, himself, meanwhile remains full of praise for the man who afforded him his first opportunity.
"I am grateful to 'Cholo' for trusting me at that time," he said. "Now, I find myself at Villarreal and he at Atletico Madrid.
"Simeone will know to understand it. He trusted me. The debut as a professional is the most important and I will be thankful for the rest of my life."
