Jamie Vardy pulled one back to set up a nervy final 20 minutes but Burnley held on to secure five straight top-flight wins for the first time in 50 years, while a return to European competition - they haven't played at that level since 1966-67 - remains a genuine possibility.
It is now a year since the Clarets were awarded a spot-kick, and Dyche said: "It's impossible, or at least improbable in modern football".
With five games of the season to go, Leicester are still targeting a top ten finish and Puel is hoping their second-half performance can carry through into their remaining fixtures this term. "Now it's open-minded and see how far we can go".
"For Burnley Football Club even to be spoken about, it's a long, long way from where we were. But I've got no loyalties to them any more so hopefully we'll have a good weekend".
"I thought (we had) a very fast start, a pretty decent first half, and then second half we started well, but 2-0 is a amusing scoreline, especially at this stage of the season".
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"They have been consistent in their play".
"After I think, like in the first half we had a lot of chances also and we came back into the game early before the break".
"I think we have at this moment, to manage the next game and to keep our ambition, but without forgetting all the good work we can do together". I was surprised because there was good concentration before the game and to concede these two goals so quickly, it was hard to accept. "The biggest thing for me is to stay focused on what we want to do". It was not a fair result.