The Merseyside club, who won at Arsenal and also beat champions Leicester City 4-1, were held to a 1-1 draw by Tottenham Hotspur at White Hart Lane following their 2-0 defeat by promoted Burnley last month.
"This is a very talented squad with a great coach," Wijnaldum, who joined Liverpool from relegated Newcastle United in July, told the Liverpool Echo.
"I believe he is building something special here. I got that feeling when I first met with Klopp.
"I knew this was the right club for me. I always had a good feeling about moving to Liverpool and things have gone well so far. I am happy to be a part of it. I feel blessed."
The Netherlands international, who scored 11 goals in 38 league appearances for Newcastle last season, is yet to open his account for Liverpool but is confident he will find the back of the net soon.
"I'm learning game by game and I think I'll continue to get better. I hope the goals will come soon. I'm trying to get in the positions to score," Wijnaldum added.
"Of course I want to score. I've always scored through the years, no matter who I've played for."
Liverpool face Derby County in the League Cup on Tuesday before their league campaign continues at home to Hull City on Saturday.
(Reporting by Ian Rodricks in Bengaluru)
