Football

Unless you are talking about teams who got knocked out of CL qualifying, in which case the answer is more complex.

Not really, I checked back to 2007 and from the list that you posted all of those EL winners didn't playing the CL qualification...

2014/15 Seville (The 4 Spanish CL teams were Real, Atletico, Barcelona with Athletic Bilbao in the playoff for qualification).
2013/14 Seville (The 4 Spanish CL teams were Barca, real and Atletico with Real Sociedad out in qualification)
2011/12 Atletico (Barca, Real, Valencia in group stages, qualifiers were Villerreal).
2010/11 Porto (The two Portuguese CL teams were Benfica and Braga)
2007/08 Zenit (The Russian CL teams were CSKA and Spartak Moscow)

[EDIT]

2006/07 Seville (4 Spanish CL teams were Barca and Real, with Valencia and Osasuna in qualification)
2005/06 Seville (4 Spanish CL teams were Barca and Real, with Real Betis and Villarreal)
2003/04 Valencia (4 Spanish CL teams were Real Madrid and Real Sociedad, with Deportivo and Celta Vigo as qualifiers)
2002/03 Porto (Portuguese CL teams were Sporting and Boavista as qualifiers)

So all that you listed didn't play in the CL (group stages or qualifiers) except:-

2000/01 Libpoo shouldn't be in your list as they lost in the QFs of the Chumps Lig.