Moore's men struck the woodwork twice through Jean-Louis Akpa Akpro and Evan Horwood, but failed to find the back of the net as Stevenage claimed a first-ever league point at Prenton Park.
There was also frustration for the hosts with 40-year-old defender Ian Goodison forced off with a hamstring problem midway through the second half.
But while Moore was disappointed with the injury and his side's failure to secure all three points he admitted he could not have asked for any more from his players.
"I can't criticise the effort or commitment. We just needed that little break or that spark when we got goal side," he said.
"It wasn't to be, but there's still plenty to build on. I'm a bit disappointed with Goody [Ian Goodison] coming off with a hamstring because that tends to only happen to sprinters, but he keeps complaining about that.
"Overall it was pretty pleasing, but I'm still disappointed not to take the three points. We just didn't get the breaks, but there was a lot of heart and determination out there.
"There's plenty to build on and I thought the crowd were good, they were patient and got behind us, and on another day it could have been three points."
Moore also took time out to praise stand-in goalkeeper Jason Mooney, who played in the absence of Owain Fon Williams.
Fon Williams was unable to make it back in time having sat on the bench for Wales' 2-1 loss in Macedonia.
"He hasn't had a shot to save all day but he's come in and kicked well for us," Moore added.
"That's two games he's played and not conceded, but at the same time it's two games we haven't won.
"That's slightly disappointing for him, but he looked solid. The pleasing thing is for me if anything happens to Fon Williams we've still got a keeper who can be a presence, no doubt about that."
Moore may have felt his side warranted all three points, but his opposite number did not agree, insisting a share of the spoils was the right result.
"Nil-nil was probably a fair reflection of the game," said Stevenage boss Graham Westley.
"Neither side had too many significant openings. They've hit our post twice and we've had two great opportunities, but I think it was a fairly even game.
"We probably had the better of the possession over the 90 minutes, but that was two sides who have worked hard and because of early season results, pleased to take a point away.
"You could see that in the overall play towards the end, no-one was really throwing everything towards it to try and get the win.
"I thought it was a fair reflection of an afternoon's work. I watched the game here last year on the television when they got well and truly put away and I was here as Preston manager the year before they were beaten, so it's definitely an improvement.
"They hit our post once or twice and we carved out a few chances, but overall I'm pretty pleased to be picking up the club's first point here."