The 26-year-old has spent his entire career at Spurs, scoring 181 goals in 278 appearances.
"With Harry, we all hope his goals and his performances will merit a trophy one way or another during his career, but Tottenham means the world to him," Rose told the Lockdown Tactics podcast.
"We know that and when you see him disappointed, it's just one of those things that when you're on Harry's team in training you win. It's not a coincidence.
"You just don't want to be on a losing side when you're on Harry's side, even in training. He's got that aura that you want to do the best you can."
Rose also revealed how the England captain gave his teammates a spurring speech in the Champions League semi-final last season.
He added: "One that sticks out is Ajax.
"He was injured but he came to Amsterdam and we were losing 2-0 at half-time, 3-0 on aggregate and he was watching in the stands.
"He came down and he just ripped into us basically. Just telling us we weren't good enough and a certain player (Frenkie De Jong) was running the show for Ajax, what were we going to do about it? We had to pull our fingers out.
"He's switched quite a few times Harry. You wouldn't think it but when he goes, he loses it, but in a good way. He wants you to do better. He wants the best for himself but also for his team-mates."