Keane said: "It wasn't a great game but I think we had the better of the chances.
"I was pleased with the clean sheet.
"We're looking a bit more solid at the back, but we're obviously not scoring enough.
"Sometimes you have to give credit to the opposition goalkeeper but I still feel we had one or two other chances.
"There was one on the line and you just need someone to have that killer instinct and put the ball in the back of the net.
"We're lacking that at the moment.
"The plus was that we kept a clean sheet, but I don't think we played particularly well.
"I always knew it was going to be pretty hard, with them playing three in the middle.
"I know our fans want us to play attractive, attacking football but it was hard to open them up.
"When you talk about the team scoring goals, you end up talking about the strikers, but it's not against the rules for defenders or midfielders to score either.
"And if you're going to achieve anything as a team, you need one or two of your strikers to put the ball in the back of the net on a regular basis."
Lee Martin had Ipswich's best effort in the first half when his scorching long-ranger was pushed away by Grant.
Carlos Edwards then screwed another effort over the bar after a cross was partially cleared into his path.
Wednesday felt they should have had a penalty, for what appeared a handball by Damien Delaney, and just after Marcus Tudgay's fierce shot from just inside the box was pushed away by goalkeeper Asmir Begovic.
Genuine chances were still a rarity but Town certainly had the best of things, only to be denied by goalkeeper Grant.
The Owls' hero made three vital saves, blocking Owen Garvan's downward volley, Alan Quinn's driven shot and then another low effort from substitute Jon Stead.
From the second of those, there was a mad scramble in the six-yard box from the ensuing corner and Frank Simek hacked the ball off the line under pressure from Walters.
Wednesday boss Brian Laws said: "I was pleased with the clean sheet and our second-half performance.
"It was a solid performance from our defence.
"I was a bit nervous when three of our back four had been booked in the first 20 minutes.
"We had to be really disciplined after that, especially on a wet surface, and if one of them had made one mistimed challenge they would have been off."
Of Grant's heroics, he added: "Goalkeepers get you points.
"When your back four has been penetrated you have to rely on your goalkeeper.
"He made two or three important saves and it would have been very harsh had they scored.
"It was a very solid, workmanlike performance from us and now we've got to build on this."