Christian Benteke's injury-time penalty, after Ben Foster brought down Matt Lowton, clinched Sherwood's first success as Villa boss.
The 2-1 result also ended a seven-game losing run for Villa and lifted them out of the Barclays Premier League relegation zone.
Sherwood felt his pulse and gestured to the Villa fans as he walked off and believes the strugglers are fighting again.
"I was saying we're alive
There were people who wrote us off but we're alive and kicking
People will look at that result but the performance was great," he said, with Villa three points clear of the drop zone.
"We need to bottle it up and experience it a few more times.
"It's the best feeling in the world
When I left home my missus said to me she had done the Euro lottery - a 54milllion jackpot - but I said I'd take three points all day.
"It shows the effort and how far we have come, we have improved every game
It was the best performance
We dictated the pace of the game in the first half and it should have been more than 1-0."
Benteke scored in the league for the first time since December and Sherwood admitted the striker had told him exactly what he would do with a penalty.
He said: "Goalscorers are there to be shot down and it takes a brave man to stand up there
I asked him before the game if he gets a penalty what he was going to do.
"He said 'I'll wait until the goalie goes down and I'll roll it in the corner'
I was still peeping through my fingers."
Gabby Agbonlahor opened the scoring and had two cleared off the line, while also having a penalty claim ignored after he beat Foster to the ball.
Saido Berahino had equalised in the second half before the late drama which left Albion 13th in the table.
But Baggies boss Tony Pulis defended keeper Foster after his gaffe cost them a point.
Pulis said: "I haven't seen it but Ben should catch it anyway
He has been fantastic for us all season, he has won us games and he has had an off night, but there'll be no one here who will criticise him.
"I don't have to speak him, he knows
We'll dust ourselves off and get going on Thursday."
Pulis also played down Alan Hutton's challenge on Berahino which saw the pair square up to each other late in the game.
He said: "I haven't seen the Hutton challenge
There has been a lot of criticism thrown at referees recently but I'm not going to go there
I'll let other people decide what they thought about it.
"The most important thing was Villa were better than us in the first half
They were quicker, kept the ball better and we wanted half-time
The second half was a different game."
Source : PA
Source: PA