A lavish close season has seen the Reds capture the likes of Allison, Naby Keita, Fabinho and Xherdan Shaqiri, raising the expectation around a side that finished fourth in the English top flight and reached the Champions League final.
Manchester United boss Jose Mourinho said this week that the Anfield side "must" win the domestic crown to justify such investments, Klopp says it is not as simple as that.
"I don't think it's a big difference [in pressure]. Only that now people maybe from [last season], they believe a little bit more, but it doesn't change the situation," Klopp told ESPN.
"Yes our job is to improve the team every year, to improve the football every year and if you do that then the chances become bigger.
"Tottenham pretty much complete, Arsenal, they lost [Jack] Wilshere, that's it, and otherwise they only brought players in, so strong side obviously.
"Everton ... big things, Wolverhampton can be a surprise. It's a difficult league, so we don't have to dream too much and we don't.”
"The circumstances are good and we have a good team. The people are happy about the team and the players we brought in obviously have quality as well. That's all good, but that alone is nothing.
"We have to use the potential and make quality of it. That's how it is and that works in different ways.
"But nothing is decided now. Everything is possible and so let's try and go for everything.
"Any trophy is good. Whatever you can get after a final, take it."
The signing of Alisson from Roma saw the Brazilian become the most expensive goalkeeper in the world, but the Reds would have had to pay even more to land fellow target Jan Oblak from Atletico Madrid.
And Klopp is happy with the arrival of the 25-year-old, saying the club saw a rare opportunity when they found out he was available.
"Everybody thinks it's a lot of money. It is a lot of money," Klopp said. "But he could've left for crazy money.
"The clause for Oblak for example is €100m, so nice! And that's it in this year where obviously a few things happen on the goalkeeper position.
"That's part of the job, to try to bring the best players you can get.
"The goalkeeper market is different because it's not each year that there is anybody available and stuff like that.
"We didn't know exactly if Alisson is available or not, but from a specific moment we realized obviously he is available and that's the moment when we decided we want to go for him.
"We are really fine with our goalkeepers. So there's no doubts Simon Mignolet -- big quality, absolutely Premier League highest-level quality, Loris Karius as well.
"Yes, we all know what happened in the [Champions League] final, but we know as well why it's not about that.
"It's not the reason. We really wanted to bring in a player which we didn't have before to be honest and that's what happened with Alisson."