Ched Evans gave the Blades a 30th-minute lead at Bramall Lane with his 26th goal of the season but Rovers came back to earn a point when Lucas Akins headed an equaliser in the 54th minute.
Moore, who has overseen an unbeaten four-match run in League One since returning to take charge, said: "Everybody probably thought we were going to get beaten but I thought we deserved a point because we worked hard and limited them to very few chances. Really, we probably had the best chance to win the game. But I think a draw was a fair result overall.
"We were always a threat from set-pieces and it was a great ball in for the goal by Welshy (John Welsh). Ryan Brunt half-went and then tried to stay up so we could have had a penalty. He'll learn because he's only a kid. If I'd have been playing, I'd have gone down, there's no doubt about that."
Moore admits he is enjoying his return to management and was eager to praise the players for their efforts since he took over.
He added: "We've got a good bunch of lads who are solid and committed. I can't fault them. It's fantastic to be back in work. I've been doing some work for Press Association Sport, which I've enjoyed, but there's nothing like being in charge of players and on the touchline."
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