Liverpool took the lead through Steven Gerrard's first-half penalty, after Phil Jones fouled Raheem Sterling in the box, but second-half goals from Wayne Rooney, Juan Mata and Jesse Lingard gave United new boss Louis van Gaal his first trophy.
"I thought it was a really good game and both teams have had a very good workout out here," the Liverpool boss said.
"I thought we were well worth the lead and had a couple more chances to increase that and it looked like maybe we should have had another penalty.
"We conceded a disappointing equaliser and then very quickly conceded another one so the game started to get stretched a bit, but overall I'm delighted with the whole tournament and what it's done for us.
"We have worked very hard and we will leave here with plenty of positives and look forward to the new season.
"The condition of the players that we have at the moment is very good. We've obviously got a few missing but certainly by Southampton we will be ready and we are looking forward to it."
The Liverpool boss was impressed by the performance of England forward Sterling, who he felt was always a serious threat during the game in Miami.
Rodgers added: "I thought he was outstanding and was a real threat. Raheem is tactically aware for such a young player and is so exciting to watch. When he runs at defenders he creates many opportunities.
"At 19 years of age he is a real talent and is getting better all the time."