Well they usually don't play their first team in Europa. And in CL Inter and Milan have struggled in their last appearances it's true.
Inter in particular had 3 coach changes in 2010-11 season and had a terrible pre-season. It was really special to beat Bayern Munich but the team was in a terrible condition and lost rather easily to an inferior Schalke team. Milan lost to Tottenham in a season they were very pathetic in Europe.
And 2011-12 was also a disaster losing to Marseille in the last 16.
I remember Parma was trying to stay out of the relegation zone and was also in the Europa League (first EL season after being changed from UEFA Cup iirc) and they were fielding their reserves and reached semis
Actually the schedules of the leagues and the way they are set have a lot to do with European success. In England, the league goes heavy during December-January. In Italy, it happens in February-March which coincides with the knockout stages of Europe. Germany has less games while in Spain it's around November-December iirc where the teams play lots and lots of game close to eachother. They've changed it in Italy this season though. But most teams are in Europa and I doubt they are interested in the competitions that much.
It's a shame because this is why the Germans have overtaken the 4th CL spot. They did a bit good in CL and great in Europa (which btw gives the same coefficient points)