Lancaster's inexperienced team ran in seven tries to complete a record 54-12 win over Fiji at Twickenham, but England were incredibly slow in the opening quarter and also failed to take all their chances in the second half.
Lancaster also admitted afterwards that the fact that his team allowed Fiji, ranked 14th in the world, to score two tries was not good enough.
Former England captain Moody, who retired from the game in March, thinks the red rose stand a good chance of beating Australia next week, but he admits their chances of overcoming South Africa and New Zealand in the other two QBE internationals this autumn are slim.
"It was a great start to the autumn campaign, but it's going to be very difficult for England in the next three weeks," Moody told BBC Radio Five Live's Sportsweek programme.
"Australia aren't in great form and they have injuries so there is an opportunity there for a win but against South Africa and New Zealand I do think England will struggle a little bit.
"The game they don't have a huge hope in at the minute is New Zealand because they are the number one side in world."
Moody lifted the Webb Ellis trophy with England in 2003, but his last act with the red rose was to lead the country through a dismal World Cup campaign in New Zealand.
Lancaster was brought in to turn England's fortunes around after the campaign in New Zealand, which was hit by criticism over the team's poor performances on the pitch and their antics off it.
Lancaster guided England to second in the RBS 6 Nations earlier this year and Moody has been encouraged by the team's progress under the 43-year-old.
"This team is coming along nicely and is moving in the right direction," the former Leicester flanker said.
"I didn't see England putting 50 points Fiji so it was a delight to see the number of tries run in and the manner the guys played after the way they started the match.
"All round it was nice to see the attacking style of play that England put out because that has been the criticism over the last few months.
"It's important to get three wins to make sure England are seeded well for the World Cup, but the style is the most important thing."
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