Although Rooney has been inspirational for the Red Devils this term with 26 Premier League goals from just 32 appearances, United missed out on title glory.
Chelsea, who scored 17 more league goals than Sir Alex Ferguson's men, clinched the top spot on Sunday with a crushing 8-0 success over 10-man Wigan.
While Giggs is against picking the bones from United's fine campaign, he believes that if one area needs improving it is that they must find more goalscorers.
The Welsh wizard has been enthused by the club's improved defensive form, but feels following the losses of Cristiano Ronaldo and Carlos Tevez that they need more threats in front of goal.
"If you had to say one thing, you'd probably say we can't rely on Wayne next season like we did this one," Giggs told the Daily Mirror.
"We need to be scoring more goals from different areas and from different players, even though as a team we scored more than we did last season.
"We were also better defensively this season than last, but we can't rely on Wayne as much as we have done this season in terms of goals.
"On Sunday against Stoke we started full of hope, then came in at half-time and found out Chelsea were 2-0 up and Wigan were down to 10 men.
"We knew then it was over and, to be honest, we didn't want to go out for the second half. You just want to go home in that situation."
United were also hamstrung in the final few weeks after Rooney damaged his ankle in the latter stages of their UEFA Champions League defeat to Bayern Munich.
The England international could never quite hit the dizzy heights that terrorised Premier League defences beforehand and Giggs believes the knock came at the worst time.
"It was unfortunate for us that Wayne got injured at a really important part of the season, because we'd relied on his goals more or less throughout it," he continued.
"So to get to the business part of the season and not have him, then to have him for one game without him having really trained, wasn't ideal.
"But whether the manager does or doesn't bring in any other strikers this summer, the other players know we need to score more.
"Whether that's defenders coming up for corners or midfielders chipping in, we all need to contribute a lot more."