Rodgers was speaking after his Premier League team had overcome a bright start from Cherries to claim a 2-0 win in their FA Cup clash at Dean Court on Saturday.
Prior to the high-profile fourth round clash, Cherries boss Howe had urged his men to stick to their passing principles and to demon-strate how they play the game.
Goals from Victor Moses and Daniel Sturridge proved enough to end Cherries’ resistance as Liverpool came through to secure victory in front of a capacity crowd.
But Rodgers then lavished praise on Cherries and dismissed suggestions that their style, and the surroundings, had been ‘too nice’ to lead to a famous giant-killing.
The Liverpool manager said: “When you have a team that want to play football, they are the most courageous players on the field.
“I don’t think it is too nice. It is easy to coach a team to just sit back, to not want the ball, to defend and then just wait for a lump up the pitch.
“The courage the Bournemouth players showed was fantastic. They have got better and better as the season has gone on.
“Bournemouth is a wonderful club and they have a great history and tradition here. Right the way through their history, they have played good football.
“In this country, it is deemed too nice but that is why we cry when we come to World Cups and wonder why the players aren’t technically good enough.
“Coaches like Eddie Howe will take the game forward in this country because they believe in a way of work and have a philosophy. I think they are a terrific team.
“There is no right or wrong way to play football but for many years in this country, the coaches who stuck their neck out and got their teams to play football were discouraged.
“There used to be a coach at Bournemouth, Sean O’Driscoll, a top coach and top manager.
"He may never get the chance to work at Premier League level but he is one of the best coaches about who never had the chance to work with players and improve players.
“It is a terrific club so I don’t think we can knock them for playing good football.”
In the lead-up to the game, Howe had described Rodgers as one of his role models.
Asked by the Daily Echo whether he felt Howe could manage at the top level, Rodgers added: “Absolutely. He is a good guy. He manages players well, he takes the pressure off players to play football and he talks with his players.
“He is someone, for sure, that will go on. He has good experience and he is improving all the time. Bournemouth is a great fit for him. He was a terrific player here, loves the club and you can see how the players play for him.
“He has a long career here in management. There is absolutely no question his ideas can be suited to the very top.”
- GRAB today’s Daily Echo for your bumper 16-page FA Cup special looking back on Cherries’ FA Cup date with Liverpool including photos, report and in-depth match reaction from Dean Court.