That means Tottenham, Man City, Liverpool and Arsenal, all in and around fourth place at the moment, could lose their Champions League reward if they finished fourth.
But Shakespeare said: "Jamie's not a cheat".
"To win the Champions League most years, and ever more so in recent times, you need three or more of those leafing players and it says something about English football that there are so few in our teams".
On frustration from joint-chairman David Sullivan after losing 3-2 at Bournemouth: "It was a comment on that game, and I said also we can't be happy with the way we performed and how we conceded the three goals".
City fans sang 'Are You Going To Madrid?' after being drawn against Atletico Madrid in the Champions League quarter finals.
"We should have shut the game out but it was a great performance all round".
"We did it and we proved a lot of people wrong".
Leicester are unbeaten in five league and cup matches against West Ham, winning four of them.
The frustration led to former Manchester City midfielder Samir Nasri, who is on a loan spell to Sevilla, headbutting Jamie Vardy in the 73rd minute and being sent off after getting his second yellow card. It's not hard - there are good memories and nice memories but that's what they are.
"We played Barca in pre-season and it would be nice to play at the Bernabeu".
Leicester reverted to the counter-attacking setup that served them so well last season when they came back out for the second half.
He has now guided Leicester to victory in each of his last four games since taking over from Claudio Ranieri.
This week saw the Champions League quarter-final draw made, with just one Premier League team making it into the last eight of Europe's top competition.
Andy Carroll needs one goal to bring up his half century in the Premier League.
The former Manchester United winger believes that there is only a handful of the world's very best players now plying their trade in the Premier League.
"It seems the very best players are concentrated elsewhere, and there is just a sprinkling of the leading players in the Premier League sides". Playing against the French side in an away game at the back of a solid 5-3 lead in the first leg, Man City expected to make it past Leonardo Jadim's side, especially with the risky striker Radamel Falcao out of the game with a hip injury.
Craig Shakespeare has won both of his Premier League games in charge of Leicester City so far - no previous Leicester boss has won their opening three Premier League games in charge of the club.