At least one English club appeared in seven of the eight Champions League finals from 2005 to 2012, but since Chelsea's triumph in Munich it is La Liga that has taken over in terms of European dominance.
This season saw another poor showing as Tottenham Hotspur crashed out in the group stages before Arsenal and Manchester City were both eliminated in the last 16, leaving Leicester City as the unlikely sole flagbearers in the quarter-finals.
"It's disappointing, but it's what they (the Premier League clubs) deserve. You've got to work hard to get there, and you've got no divine right to make the semi-final. Hopefully next year it will be better, but what you have to realise is that the English Premier League is the most demanding league in the world," Rush, who is an ambassador for the tournament, told PA Sport.
"It's very difficult to do well in that and also do well in the Champions League. You need a strong squad to do that. I'm very biased but I said from day one my dream final would be Juventus against Real Madrid for obvious reasons. I played for Juventus and I'd like to see Real because of Gareth Bale.
"All the Welsh public want to see Real there because they want to see Gareth in the final, that would be a dream come true. But it's not going to be easy for them because Atletico are a very good working side. Real are favourites as they've got more world-class players, but don't underestimate Atletico because they work really hard as a team and that's sometimes the secret of success."
In addition to the all-Madrid semi-final between Real and Atletico, Juventus will take on AS Monaco in the other last-four clash.