United claimed their first silverware of the David Moyes era when they defeated Wigan 2-0 in the Community Shield.
The victory has eased some of the tension among Red Devils supporters, who had started to become agitated by a combination of poor pre-season form and the lack of fresh blood since Moyes' appointment was announced in May.
However, as Moyes confirmed after the Wembley encounter, he is still trying to bolster his squad, knowing time is ticking down until the window closes on September 2.
With Arsenal equally bereft and high-profile situations involving Gareth Bale, Luis Suarez and, much closer to home, Wayne Rooney still to resolve themselves, there is still evidently plenty of business to be done.
Clearly, Giggs does not have a crystal ball to know who will end up at Old Trafford, with Luka Modric and even Bale still being talked of as potential signings in addition to Everton duo Marouane Fellaini and Leighton Baines.
But he does know that with all but Paul Scholes still remaining from a squad that clinched the title by 11 points last season, United will remain in a strong position.
"The quality is in the squad," Giggs said. "We showed that last year. Now we have to show it again.
"It has been a slow transfer window. Manchester City did their business early on but, other than that, there has not been a lot of movement so it could be a hectic last two weeks.
"We will just have to wait and see how it goes but we are quite happy with the players in our dressing room.
"We won the league with those players so we are looking forward to the start of the season.
"If we sign someone - great. If not we will just get on with it."
Although Giggs accepted pre-season campaigns are based around the need to get fit, with just two victories in seven matches prior to yesterday's win, the Welshman knew improvement was required.
To an extent, United got it, even though the game itself was a largely forgettable encounter punctuated by Robin van Persie's brace.
There will be no opportunity to build on the result at the Aon Training Complex though, with Moyes' players now disappearing on international duty, ensuring meaningful preparation ahead of Saturday's opening game at Swansea will be limited to a single session on Friday.
"It is always hard with the internationals," Giggs said. "You don't know what you are going to get back.
"In some ways it can help you. Players need games and they are getting them.
"We need to be ready for Swansea because they have been in good form and it is always a tough game at their place."
It is the start of a tough run of fixtures for United, who must also face Chelsea, Liverpool and Manchester City in the opening five games of the season.
That stiff beginning to their Premier League title defence probably explains why United are presently third favourites for this year's championship, although Giggs said: "It is not something we are worried about.
"We are the champions. We know it is always hard to defend. But we have experienced it before and we will try and do it again this season."