The Old Trafford legend has also highlighted what the Red Devils need to do in order to catch Chelsea next season.
United were, of course, missing from this season's Champions League campaign after a poor showing under David Moyes last year saw them fail to secure European football of any sort.
That ultimately led to Moyes' sacking and the appointment of Louis Van Gaal, who can claim his first year in charge has been a success as he has met the remit of returning to the Champions League - albeit they will have to make it through the qualifiers in order to reach the group stage.
Giggs, though, says it is odd for the club to be celebrating fourth given their successes in the past.
“It feels a bit strange when you’ve been at this club for such a long time during such a successful period to be celebrating a Champions League spot,” he said.
“But, if we’re honest, that’s what we set out to achieve at the beginning of the season and going from seventh to getting in a Champions League place is great. But next year we want to kick on and be competing for trophies.”
The former winger has also given his views on what the club will have to do in order to catch Chelsea next season.
Jose Mourinho’s side have run away with the Premier League this season, performing consistently throughout to secure their first title in five years and the first of the Portuguese manager’s second spell in charge.
Many, though, are expecting a stronger challenge from their rivals next year, namely Manchester United and Arsenal, and Giggs says his side must find consistency if they are to compete with the Blues for top honours.
“Chelsea are the best team this year without a shadow of a doubt,” he added.
“We just perhaps not had the consistency, that’s been the difference. We’ve dropped silly points and to win the Premier League you can’t afford to do that. We’ve proved that we’ve got the quality, but next season we need to get that consistency.”