The Reds inflicted a 9-0 defeat on the newly promoted side after failing to win any of their first three matches of the season.
Liverpool were up 5-0 before half-time and added four more after the break, with Roberto Firmino, Luis Diaz, Trent Alexander-Arnold, Harvey Elliott, Fabio Carvalho and Virgil Van Dijk all getting on the scoresheet.
The win saw Liverpool join Manchester United and Leicester City in the record books with the biggest Premier League victory.
Klopp says his side simply kept going in their quest for more goals but not to humiliate their opponents.
"We wanted to show a reaction. Be ourselves. Getting to be the best version of ourselves. We play a specific way," Klopp said in quotes reported by BBC Sport.
"We scored wonderful goals. The game settled and we kept scoring. It was about keeping going. Not to humiliate Bournemouth, we couldn't respect them more. It's about putting the opponent under pressure.
"I could bring on the kids, they deserve it so much. Harvey is a special player, wonderful goal. Everything was perfect pretty much."
Liverpool are next up against Newcastle United on Wednesday and Klopp expects Eddie Howe's side to provide a stiffer opposition.
"Wednesday [against Newcastle] will be different," Klopp added. "Today the mix of great weather and fantastic football, we don't have that often at Liverpool so we should cherish it.
"At least we don't have to answer the question anymore [about not winning]. A really good day for us. We won't get carried away.
"If we want to be successful in this league, we have to show consistency. That's what we have to do now. That used to be our strength. We'll watch Newcastle tomorrow [Sunday, against Wolves] and see what we can do against them."
