Slot has the unenviable task of succeeding Jurgen Klopp but got off to a winning start by beating newly-promoted Ipswich 2-0 on the opening weekend of the Premier League season.
Liverpool are the only side in the English top flight yet to make a single signing in the window.
Spain international Martin Zubimendi rejected the opportunity to leave Real Sociedad, while a deal for Valencia goalkeeper Giorgi Mamardashvili is reportedly close that would see the Georgian stay at the Mestalla this season on loan.
"I trust the team," said Slot on why he is not stressing about the lack of new signings.
"I've said before, I have inherited a very good team, with young players. We trust them a lot. They proved that they have earned our trust."
Slot takes charge of his first competitive game at Anfield on Sunday when Brentford are the visitors.
The Dutchman, though, said he was too focused on getting the three points to feel the nerves of having to impress the home fans.
"I am not nervous at all. Certainly not at this moment because I'm in the middle of preparation, prepare the team for Sunday," he added.
"It wouldn't be a good thing if you have nerves. I trust what me and my staff do to prepare the team in the best possible way. I trust the team a lot."
Liverpool's window has been more dominated by sales.
Sepp van den Berg and Fabio Carvalho have joined Brentford for combined fees of close to £50 million, while Bobby Clark has joined Red Bull Salzburg.
England defender Joe Gomez has also been linked with a move away before the transfer deadline in a week's time.
The 27-year-old appears to have fallen down to fourth choice centre-back but Slot is keen for him to stay put.
"At this moment I am expecting everyone to be here. (But) everything can change," said the former Feyenoord boss.
"He didn't play a lot in the Euros and when he came back in the first sessions he couldn't train the whole session, so we had to manage his load and that was also a bit (of) a reason why he wasn't in the team on Saturday.
"But this week he had a good week in terms of load and how much he could do with the team.
"He is one of the players that I see new things from and learn things what I see from him."
