Wednesday did well and just a bit of naivety in midfield made sure The Toffees capitalised on The Owls' mistakes and went back to Merseyside with a comfortable-looking victory on paper.
But with Jermaine Johnson, Deon Burton, Graham Kavanagh and Glenn Whelan all going close for the home side, it was not to be.
Laws said: "It's a disappointing score line because it doesn't really reflect the true story. I am sure Everton will be pleased to win the game and get three goals but that is disappointing from us because for 75 minutes we were right in the game.
"During the first half, we looked comfortable and didn't really come under much pressure. We looked like we could hurt Everton at times but we chose the wrong pass at the wrong time in manufacturing stages of a clear-cut chance.
Everton boss David Moyes heaped praise on The Owls by saying: "I would say though that Sheffield Wednesday gave it a real go and were difficult opponents. Sheffield Wednesday's a terrific football club, a 'Premiership' club - and to come here and win was never going to be an easy task."