Christian Benteke set the ball rolling with a neat 16th-minute shot from Leandro Bacuna's pull-back and after Gabriel Agbonlahor had helped himself to a double, followed suit a minute before the break with a powerful header which gave bemused goalkeeper Costel Pantilimon no chance.
The defeat saw Villa leapfrog Sunderland, who are now in 17th place and just four points clear of the relegation zone.
However, there was support for Poyet from former Tottenham team-mate Sherwood.
He said: "It's not great, is it, when you are beaten heavily at home, but Gus will bounce back. He's that type of character who has seen it all and done it all before.
"There's one thing Gus has got, he's got a bigger heart than anyone."