Let me remind you that Lester won two games in the Championship, twice in the last season the teams played in a draw, and also with one victory, in a match of the first round, Bournemouth was remembered.
Despite achieving their highest league position in their 118-year history, Howe believes there is plenty more to come from this Bournemouth side.
Jamie Vardy netted his 16th goal of the season to secure a point, which left Leicester 12th in the final table, following Junior Stanislas' opener after just 57 seconds.
Although Leicester were thrashed 6-1 here by Tottenham Hotspur on Thursday there was a festive mood around the King Power Stadium before kickoff and not only because the club's chairman, Vichai Srivaddhanaprabha, arranged for free beer and programmes to be distributed to fans.
Claudio Ranieri has given his seal of approval to Rafa Benitez.
Craig Shakespeare says he will wait to sit down with Leicester's owners before discussing his future at the club, but has given no time-frame on when the meeting will be.
Injuries meant that Shakespeare had little choice but to deploy the same defence that had been ridiculed by Spurs, and Bournemouth quickly inflicted more embarrassment.
Lys Mousset turned Christian Fuchs inside out to burst into the area and continued his run after Ryan Fraser was taken out by Danny Simpson. His weak shot deflected off Ben Chilwell and into the path of Stanislas to slide under Kasper Schmeichel from 10 yards.
It look Leicester half an hour to find their feet. The home fans began to groan and Shakespeare must have anxious about the effect a limp performance was having on his job application.
Bournemouth's resistance was broken soon after the interval.
Allsopp tipped over a header from Vardy and Slimani had an unbelievable chance to win it five minutes from time but his header went past the far post, with the goal gaping.
Leicester nearly grabbed a leveller five minutes before the break when Yohan Benalouane's shot deflected just wide and Islam Slimani nodded the resulting corner across goal.