Despite suffering just one defeat across three competitions under new manager Arne Slot, Tsimikas says the squad remains humble as it is early in the season.
He told the club's website: "It's very early in the season, you can't say in one department we are very good or in another department we are very bad.
"I think we have to improve in every department every day if we want to be successful.
"My opinion is that we are in the right way. I think we have to improve in every department. If we want to win football matches, always we have to improve to play better if we want to achieve our goals.
"I think we perform well – it's very important to continue like that. I think the future will be hard, as the start has been. I think everybody is ready for these challenges ahead. We have to go for it."
After a well fought draw with Arsenal, the Greece international opened up about how Liverpool must take the point especially after being behind twice against Mikel Arteta’s side.
"We take the one point and we have to deal with it," he reflected. "It's a very tough place to go, it's a very good team.
"Twice we were down and at the end we took the point. We have to deal with that, we have to take the point, we have to continue. We have to play better football to win football matches.
"I think the result at the end was fair for both of the teams. We take the point, we deal with that and we go for everything we have ahead. We want to win more games.
"(Arsenal) are a very tough opponent and it's a very tough place to go and play. We take the point."