The Dutchman was named Pep Guardiola's assistant manager at City a year after leaving the same role at Liverpool under Jurgen Klopp.
After City's impressive win at Wolves for Saturday's Premier League opener, Carragher said Sky Sports: “It's one game, I can't get out of my head what Pep said last season, that ‘it's not really my football where the game is going’, transition, end-to-end football.
“Pep Lijnders is a big coach, big influence on Jurgen Klopp and I did see little instance of that Liverpool team. I watched the game at the weekend and couldn't believe what I saw, the players were jumping a high line.
“When you think back to Liverpool and the amount of counter attacking goals with Sadio Mane and Mo Salah - I looked at the goal from Reijnders who was an absolute revelation - and - it was maybe not much like a Pep Guardiola goal.
“Of course they've scored plenty of counter attacking goals in the past but the reason it stood out was the counter attacking nature of it and the celebration, Lijnders and Guardiola, he's giving him the thanks hug.
“We don't know exactly what it's for but I don't think it's a coincidence, he as a coach is having a big influence on Pep Guardiola.”