The Hatters went down by a single-goal margin for the second time in five days, following Tuesday nightās last-gasp 4-3 defeat against then-Premier League leaders Arsenal.
This time Town took the lead on the stroke of half-time, through Elijah Adebayoās far-post header, before goals from Bernardo Silva and Jack Grealish turned the game in the European championsā favour.
Edwards said: āWe were aggressive and on the front foot against probably the best possession-based team there is in the world, and we took it to them. Thatās what we wanted to do, and then when we had the ball and had opportunities, we were brave again and showed the best of ourselves.
āI thought we were excellent, I really did. I loved so much of what our team was about today, and we are all really disappointed that we didnāt get something from it and get that reward.
āBut I think we can all recognise the size of the challenge, this whole week, so I think we can all be very, very proud of these players and what they are giving to this football club.ā
He added: āOur challenge now is to obviously maintain these high standards going into every single game, and the points will come.ā
On Adebayoās goal, his second in as many matches and fourth of the season, Edwards said: āElijah has deserved his opportunity, heās working very hard. Heās difficult to play against when heās like that, when heās on it, as he has been.
āHe is that goal threat and itās great, because the good thing is we look a threat from however it is.
āIf we have a little bit of possession as we did today, if itās from a set piece, if itās a counter attack, weāve got the players to score and maintain a threat in the games, and that should give us a lot of confidence against top teams as well.
āIām pleased with the whole group and how hard theyāve worked, but I know Eli will get some of the headlines because of his goal. It was a fantastic header.ā