Craig Westcarr put Walsall in front after only two minutes, driving in a cross from Adam Chambers, and Slovakia Under-21 international Miklan Lalkovic, making his debut on loan from Chelsea, drilled home the second in the 25th minute.
Rovers skipper Andy Robinson pulled one back with a superb free-kick five minutes from half-time, but the Saddlers made sure of the points with a four-man move ending with Westcarr clipping home the clinching third goal.
Moore said: "This is a tough league and if we perform like that at Wolves, Bristol City or Peterborough it will be five, six or seven.
"They (Walsall) should have been out of sight in the first half. We cannot play and defend like that.
"Our keeper (Owain Fon Williams) had to make far too many saves. We made it 2-1 before half-time and could have made it 2-2 later, but it would not have been right because that performance was unacceptable. It was gutless.
"Our full-backs went too long with the ball which is not our way of playing. We are a footballing side. We knew how Walsall play. They are not a physical side and want to get it down and play."
Moore praised his keeper, Fon Williams, and midfielder Robinson, adding: "I know its only the first game of the season, but its worrying when we perform the way we did."
- Sports & Recreation
- Craig Westcarr
- Adam Chambers