The East Midlanders were leading the Gunners 3-2 going into the final 10 minutes of Friday's 2017-18 Premier League opener, thanks to a Jamie Vardy brace and a Shinji Okazaki strike.
However, Arsenal struck back via substitutes Aaron Ramsey and Olivier Giroud, in the 83rd and 85th minutes, to leave Leicester facing a trip back up the M1 empty-handed.
Shakespeare told Sky Sports News after the game: "We've had this a few times here. To lose in the manner we did is very disappointing. We can take heart from the way we went about it but in those key moments we needed to be a bit more streetwise.
"Arsenal had a lot of possession and have world-class players. We showed what we're capable of, showed heart and spirit. We've got a challenging start but if we get this type of performance then we'll get points on the board."
Leicester lost at Arsenal last season due to an 86th-minute Robert Huth own goal, while Danny Welbeck's injury-time strike at the Emirates in February 2016 had threatened to detail Claudio Ranieri's ultimately successful title bid.