Matter of fact I looked back at the noughties and from memory + a bit of blanket research this is how it stacks up for me:
00/01 - Bayern, Real, Valencia, United, Super Depor, Ancelotti & Zidane Juventus, Leeds (their last great side with Fowler and Ferdinand) + also early Meelan, Arsenal, Roma winning Serie A with Batistuta, Newcastle is in there, a blip by Anelka at PSG and slow rise of Leverkusen with Ballack, Berbatov, Lucio et al
01/02 - Real, United, Bayern, Lippi Juve, Ancelotti improves at Meelan and the time of real Milan derbies vs great Inter, peak Rivaldo Barca, Arsenal joins title talk, Newcastle still there, Leverkusen a top Monaco-like year, Super Depor consistently beating Real and Barca at home
02/03 - Milan, United, Juventus, Real (these sides were all so good it's difficult to rank without stat info), Valencia, Arsenal, Hitzfeld Bayern ends with a shocking campaign, last Shearer years at Castle, Super Depor continues
03/04 - Milan, United, Arsenal Invincibles, Benitez Valencia wins Liga, culmination of Super Depor with the Milan upset, mad year with Giuly & Rothen Monaco, Ranieri Chelsea with a great run pre-Abramovich takeover, Real curse of R16 starts from hereon after Morientes buries us, Ronaldinho arrives at Barca
04/05 - peak Milan, Jose Chelsea choke semis vs Liverpool, Barcelona well and truly back, Cristiano arrives at United, Juve continue to win Serie A (titles stripped by Calciopoli), Lyon cement their spot as a tough nut to crack, Germans wiped off the grid, Hiddink PSV with a great year
05/06 - Barcelona, peak Milan, Chelsea, Arsenal, United oddly choke their CL group, Inter continues to rise, Pellegrini-Senna-Riquelme Villarreal sensation year
06/07 - Milan's final great year, Cristiano Ballon DOr level United, demise of Jose at Chelsea, Ibra arrives at Inter, Arsenal and Liverpool kinda up there but not really and starting their wishy-washy period, Barca cock it up, Lyon still romping Ligue 1 and challenging in CL, Germans still dead and buried for the most part but Makaay scoring vs Real in 1st minute was funny
07/08 - peak United with CR and SAF with nobody really on their level other than a flukey Chelsea side, Barca drunkenly staggering to a semi, Milan drop off, Inter nearly there on top level
So maybe not as drastic as the 8-10 I mentioned, but pretty close.
Liverpool is nowhere near Barca 08-12 or Milan 02-07 in comparison. Like, not even scraping the barrel. They may get there, but it's very difficult to determine whether this is actually their era starting.