The forward's first-half stunner sent the Reds into the fourth round to face Brighton.
The 1-0 third-round replay win at Molineux stopped their slide after Premier League defeats to Brentford and Brighton and a fortunate 2-2 draw with Wolves in the original tie.
Liverpool now host Chelsea on Saturday sitting ninth and 10 points adrift of the top four.
"The last few results haven't really gone our way, we haven't performed to the best of our ability, but I think it is a stepping stone for the next couple of games," Elliott told the club's official site.
"We just need to take this into the next game on the weekend. It's going to be a tough one but this is the perfect way to go into the next game. We're full of confidence and hopefully we can put it right at Anfield at home in the Premier League.
"It's a stepping stone, as I said, hopefully we can go in there fully confident and hopefully get another good result at the weekend - we just focus on the next game and as they come."
Wolves failed to seriously test Reds goalkeeper Caoimhin Kelleher despite an improved second-half display, as they are left to focus on survival.
They announced the signing of Pablo Sarabia from Paris St Germain ahead of the game as boss Julen Lopetegui continues his recruitment drive to keep the club in the top flight.
"He's going to be a good player, a good help for us, of course. In the next days he's going to start working with us and we are happy with one player like this," said Lopetegui.
"He's here because we believe in him and he's going to be a player that I'm sure is going to help us to achieve our main aim, that is to be out of the relegation zone at the end of the Premier League.
"Now, we have to change our mind, to put the focus only in the Premier League and this is all."