United bowed out of the competition early last season after shock losses to Benfica and Basel but sealed their spot in the next stage this time round with four wins out of four after the victory over Braga.
Giggs was delighted with the manner in which the team bounced back from a disappointing European campaign last season.
"We were all disappointed [last season]," the Welshman told Sky Sports.
"It wasn't good enough. We knew we had to do something about it and we have.
"We hope this continues now. We're in good form, both in the league and the Champions League, so we have to carry it on now."
The veteran Welshman also praised striker Robin van Persie, who came on in the second half and sparked United to a late comeback with a goal in the 80th minute goal.
"Robin gets one chance and he puts it away," Giggs added.
"He's just scoring goals for fun at the moment. With the form he's in, his confidence is high and I think everyone knew he was going to score."