Leeds United started brightly and thought they had taken an early lead through Dominic Calvert-Lewin, only for VAR to disallow the effort for handball. Bournemouth subsequently capitalised on a costly James Trafford error, with Evanilson scoring in the 31st minute before Amine Adli added a second in stoppage time.
Rose acknowledged that his team had been forced to work hard against an opponent who initially matched their intensity.
“We knew that it's going to be a different challenge today against a really good opposition. Leeds matched up our intensity. In the first 10, 15 minutes they were even better in this part.
“We lost some duels and then we conceded the goal. It was not given, lucky us, and then I felt that we got a little bit better into the game and then we rewarded ourselves for our front-footed approach.
“We won a high ball and scored an easy goal. But it's hard work.
“And then it was an open game, open fight, and at the end we had Junior with a top assist and Amine with fresh legs who just finished the game.
“So, difficult game, difficult opponent, and I'm really happy that we solved the challenge.”
The Bournemouth manager also explained the difficulties of managing his squad during a demanding schedule, with fixtures coming every few days.
“I mean, we play every three days so far. We have to get used to it as a club, as a team, even we changed a lot.
“So it means some players like Adri [Truffert], they didn't play 90 minutes in midweek, but we had not a proper training this week because we played.
“So it's part of our season, part of our job we have to do, and the most important thing is that we stick together, that we adapted a couple of things in the half-time and that we fought back.”
Farke was considerably less satisfied with the outcome, believing Leeds had produced an excellent performance for long periods but had been punished by one costly mistake.
“Most important is the result and of course we're disappointed that we travel away without points. Football is brutal sometimes, it can feel like the most unfair sport in the world. One goal is very often decisive.
“We would have deserved so much more. First 30 minutes we played fantastic football, created chances and scored one of the best team goals of the season. Out of nothing they were in the lead because we scored more or less an own goal.”
Farke felt Bournemouth's defensive organisation made the task increasingly difficult after Evanilson's opener.
“They're so well structured and if they're 1-0 up at home and can concentrate on defending and counter attacking it can be very difficult.
“It was an own goal, we were 1-0 down and this was decisive. They could concentrate on sitting really deep. To open a very good and really well structured Premier League side, one of the best at defending, six clean sheets in a row, perhaps we don't have the individual quality for a moment of magic.”
The Leeds manager also defended Trafford, insisting the goalkeeper retained his complete confidence.
“James is a terrific young goalkeeper, he's been outstanding so far. He has saved us points and will save us points.
“In general we win together, we lose together. For me he's still top class and has all my trust and love. My recommendation is he shouldn't watch the scene back. Football can have annoying days. We won't dwell on it.”