Neither of those are still gracing the competition, with Leicester City the last British team standing at the quarter-final stage.
While the Gunners and City will be disappointed with their respective showings, Giggs feels they at least boast players of the calibre required to compete at that level.
The Welshman is, however, concerned by the lack of top quality talent acquired by British sides in their ongoing attempts to conquer the continent.
The two-time Champions League winner told The Telegraph: "It has been a factor throughout the performances of English teams in the Champions League that the quality simply is not there any longer, or not as it was when English clubs had that good run in the competition from 2005 to 2012.
"It seems the very best players are concentrated elsewhere, and there is just a sprinkling of the leading players in the Premier League sides.
"Aside from Sergio Aguero and Alexis Sanchez it is hard to think of the world-class players in the English Champions League squads this season."
"To win the Champions League most years, and ever more so in recent times, you need three or more of those leafing players and it says something about English football that there are so few in our teams.
"It is not as if the money is not there to buy the best players, it just seems that the recruitment has not always been right."
Questions have also been asked of Sanchez and Aguero this season, with the former yet to commit to fresh terms at Arsenal and the latter sparking exit rumours after being benched by Pep Guardiola.