The victory took England to the top of Group H but Welbeck, who slotted two goals to bring his England tally to eight, will now miss Tuesday's crucial showdown against Ukraine in Kiev after having already been booked against Montenegro.
Hodgson criticised Slovakian referee Ivan Kruzliak for his decision to warn Welbeck in the first half for kicking the ball away after the whistle had gone. He said: "The booking for Danny Welbeck has overshadowed the night, that's for sure.
"I don't think there'll be too many people, even in the refereeing fraternity, who will say that was a clear yellow card. A 40 yard sprint, a ball that arrives on your foot, a split second between the whistle blowing and the shot.
"You'll have to try very hard to persuade me that was a booking. He's out of the game. We'll live with it, deal with it, but I'm not prepared to go down that route that these things happen. I didn't think it was a correct decision.
"The other one he got in Montenegro, we should have had a penalty and he was booked for diving.
"He's been unbelievably unfortunate. We have already lost Wayne Rooney and Daniel Sturridge and it makes life difficult for us. It takes the gloss off a good team performance.
"But we're getting used to dealing with misfortune. The players dealt with the blows we suffered in terms of injury before the game. I hope they do the same thing in Ukraine."
Captain Steven Gerrard opened the scoring and Rickie Lambert scored his second goal in two games as England brushed aside a limited Moldovan side to leapfrog Montenegro on goal difference.
Both sides have 15 points but England have a superior goal difference and have played a game fewer. Ukraine, however, are one point behind having played the same number of matches.
With Welbeck suspended, Hodgson took off left back Ashley Cole, who was also on an earlier yellow card, and also replaced Arsenal midfielder Jack Wilshere on the hour as a precaution in readiness for Kiev.
Hodgson, however, refused to give up on Liverpool striker Sturridge recovering from his injury problem in time to face Ukraine.
He said: "It's under a week since he finished against (Manchester)United and five days since the scan on the thigh strain. You need seven to eight days. It's not impossible. We shouldn't give up hope. But is it more than 50-50? Definitely no. I would even fear it's worse odds than that. But he's coming in tomorrow night and we'll assess him on Sunday."
Lambert could be given the striking task in Ukraine in what would be just his third international performance and Hodgson also hinted that Manchester City's James Milner, who came on as a second-half substitute, could be included as a more defensive replacement for Welbeck.
Hodgson said: "We know what James will do. James isn't and doesn't pretend to be as exciting as some of the wingers we sometimes use these days.
"The game in Kiev is going to be a game where we need the experience, the strength and the quality. Milner is not a winger, but the qualities he brings could be very useful for us."
Moldova's coach Ion Caras was happy to concede only four goals against an England side he predicts will qualify for Brazil.
He said: "Considering the superiority of England I believe the score was less than they were capable of scoring, but some of the goals were due to our mistakes.
"England have considerable value and on our team there is an inferiority. Because of that you could see the score. I would like to congratulate England on their victory.
"In my opinion Ukraine and England will qualify."