The Cherries held a four-goal advantage against 10 men and were cruising to a resounding victory when they conceded twice in the final three minutes.
Howe was pleased with the overall performance, which leaves his team with 10 points from five Premier League games, but feels they should have closed the game out more comfortably.
"I think the leadership qualities when the moment happens when they score their first goal, we needed a better reaction," said Howe.
"I think we'll look at that period onwards and certainly the mindset of the team should be to try and keep clean sheets and, with an extra man, ram home that advantage.
"And I don't think we used the ball well enough when we had the extra body, so stuff to focus on.
"I think the beauty is we win the game but we learn a lot from the last period which will stand us in good stead for the rest of the season."
Ryan Fraser's double plus Joshua King's penalty and a goal from Adam Smith had Bournemouth in complete control at the Vitality Stadium.
Leicester, who had captain Wes Morgan sent off for a second bookable offence at 3-0, showed some resilience and made the scoreline more respectable thanks to James Maddison's spot-kick and a header from substitute Marc Albrighton.
The Foxes began brightly on the south coast before they were caught out twice on the counter-attack as the momentum swung in the hosts' favour.
City manager Claude Puel says his squad need to unite to bounce back from the defeat.
"We have to correct all this together and it will be important to find a solution because I think it's a shame," said Puel.
"For the next game, of course, it will be important to correct defensive aspects and our concentration and focus.
"Of course, to continue to move on – this is important."