The 20-time English champions, a record, finished fourth in the table behind Chelsea, Manchester City and Arsenal during their first campaign under Dutchman Louis van Gaal.
"We've had a pretty good start and are back in the Champions League, which is exciting," said Giggs when asked about how the team had fared under Van Gaal's leadership.
"I think we can achieve a lot as we have shown this year we are capable of matching the best teams in the league.
"Now we just have to work on our consistency, and if we get off to a good start next season we can definitely do that."
After a glittering 24-year playing career on the United wing, Giggs says it takes a different mindset, now he is into management.
"The biggest thing you learn going from player to coach is not to think like a player any more, but to think like a coach," he told manutd.com.
"As a player you're pretty selfish - you want to do well and you know what you're capable of doing and how to get it.
"I wanted to be the best as a player and I want to be the best as a coach. That means working hard and doing everything you can to achieve that but also enjoying the challenge.
"You need to get the best out of 25, maybe 30, different individuals so you need to find what makes them tick and how you're going to get the best out of them."
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