Manchester United, Liverpool and Chelsea have won the Champions League in the last decade but there were no Premier League sides in the quarter-finals of the competition last season - a scenario which also occurred during the 2012-13 campaign
And Lineker believes the hectic festive period and frenetic pace of the English game is hampering Premier League sides in their quest for Champions League and Europa League glory.
"We completely kill ourselves in the Christmas period with the madness of our fixtures
Boxing Day, New Year's Day, okay, do that, but why the middle Saturday as well? Get rid of that one and replays in cup competitions," the Match of the Day and BT Sport presenter was quoted as saying by several national newspapers
"You've got to remember as well that our football is more frantic than in other countries like Spain or Germany, so we don't really help ourselves
You come to February and all the other major countries have had a little break but we've been going bang, bang, bang
"You could see it last season with Chelsea, they are a better team than PSG but looked shattered (in their Champions League last-16 tie)
You're going to get the odd game where half-a-dozen players are dead on their feet and that's what happened.
"Whilst in the past we have been successful, but nothing like as successful as were when it was a straightforward knock out competition, one or two of our successes have been quite fortuitous in the Champions League
"I'd like to see us do better
We can compete but we don't help ourselves, and it's the same with international football.
"We've got a good league, it's quite entertaining, but it's not really thought out in terms of Champions League and international football."
Source : PA
Source: PA