Antonio Valencia, Robin van Persie and Wayne Rooney all scored inside the opening quarter of the game as United made it four wins in a row in all competitions.
However, Moyes was forced to replace Rafael, Jonny Evans and Tom Cleverley at the interval and the United boss conceded it disrupted his team's rhythm.
Regarding the injuries, Moyes told Sky Sports: "There were four injuries actually as Patrice Evra had an injury as well.
"Jonny Evans' back seized up, Rafa had gone over on his ankle and Tom Cleverley got double vision, so we ended up having to make the changes at half-time.
"It never helps the continuity coming back out for the second half, and we didn't play as well in the second half. Nevertheless, we were always worth of a victory."
Moyes added: "The first 20 minutes, we were absolutely outstanding, we really were. There were great goals, great movement for the goals, and we played very, very well.
"We knew it would be tough because Fulham were coming off a bad result last week and we expected them to start brightly.
"We got off to a great start and the goals allowed us to relax a bit more.
"I must give a lot of credit to Fulham, who kept going even at the end of the first half and did their manager proud with the performance in the second half."