Rasmussen joined the Twins on Friday after pitching coach Neil Allen was suspended following his arrest early Thursday on suspicion of drunken driving.
Rasmussen, who has been in the Twins organization since 1991, said he would adjust to the players, rather than the other way around.
"Mainly you come in and see what these guys' routine is and get along with them because they're used to going on a certain time and doing it," he said before Saturday night's game in Seattle. "So, you're going to stick with that because that's been established and players are creatures of habit. So, just go along with them, what do you want to do and let's see if I can help you do that."
In his first game with the Twins on Friday, Rasmussen watched rookie Pat Dean shake off a first-inning home run and pitch seven effective innings for his first career victory, besting Seattle ace Felix Hernandez 7-2 before an enthusiastic crowd of more than 40,000.
"He's really good with that," Rasmussen said of Dean's ability to put the home run behind him. "He wasn't too happy, but you give that guy the chance to run that 360 feet around there, and then by the time you get the ball back, it's time to go again. Geez, he did a good job"
Twins manager Paul Molitor said it was fun to watch Rasmussen enjoy his first game in the new role.
"For a guy who's been around the game as much as he has and big league experience, you could still see that it was kind of fun for him to be in there, especially watching one of his kids go out there and pitch the way he did," Molitor said.
"There were a couple times we had to kind of discuss where we're at and what we might do and he had his opinions, which is good," Molitor said. "It worked out, so I don't see any problems there at all. It was kind of fun to be a part of watching him be in the dugout and us going out there and having a good game on the pitcher's mound."
Molitor said there is no timetable yet for Allen's situation.
"I talked to Neil today. I'm going to try to stay in touch as much as I can. He's doing well, all things considered," Molitor said. "I think it's kind of an ongoing deal as far as where this thing is going to get steered toward. The club has its policies and protocols and we'll follow those and he's on board with all those things that he needs to be getting done before we can get him back."
Rasmussen said he's just trying to control what he can control and do what's best for the organization.
"I'm trying to do what I do and just do a good job and have a positive impact," he said. "I'm here right now, that's about it. I'm just trying to focus on tonight's game."