Let's face it, it's a league that's there to be dominated by anyone with above the average Scottish team's net spend. If you look at net spends there among teams in the SPL, it's like going back 20+ years in this league, that's how far behind it is with many teams.
He's done better than most managers have there, because he's not only dominated, but he's annihilated the opposition and completely wiped the floor with the league and cups. That's an achievement in itself.
But... the gulf in class between their standards and most top six teams from other European countries, is astounding. They have generally always struggled, bar that spell about 15 years ago when they had the likes of Davey Thompson, Hartson etc, they did quite well against quite a few big European teams (they beat us too remember). So the capability is there for them at least to enter European competition and be a bastard team to play against, but they are typically tippy/tappy under Rodgers, without the ruthlessness to then role their sleeves up and give a decent European team a tough game.
His European record is pretty symptomatic of his flaws here, too much emphasis on attractive play and a complete lack of guile and guts.