The Foxes came into Tuesday's return leg of their last-16 tie trailing 2-1, but prevailed 3-2 on aggregate thanks to goals from Wes Morgan and Marc Albrighton, their place in the quarter-finals secured by Kasper Schmeichel's penalty save from Steven N'Zonzi with 10 minutes to go.
Since Claudio Ranieri's sacking, Shakespeare has won all three of his matches in charge of the Premier League champions - this his first since it was officially announced he will lead the team until the season's conclusion.
"Immense. The players can be immensely proud and the club in general, to pull off a result like this," Shakespeare told BT Sport.
"We went in to be competitive but I thought we were immense. We rode our luck at times but the character the players showed was immense and there for everyone to see.
"These players enjoy pressing from the front. The idea was to try and make it as uncomfortable as we could. We set the game plan out tremendously.
"Goals change games and Wes gets the first one and puts us in the driver's seat.
"[Schmeichel] is a great shot-stopper, when we needed him most he came up trumps.
"It'll be nice to pit our wits against someone else, we've just knocked out one of the best teams in Europe. Their credentials are there for everyone to see. As a club we can be immensely proud.
"The Champions League music ignites everyone and the crowd were terrific. It's only three games and somewhere along the line there might be a hiccup but I'll enjoy tonight."