The Italian was sacked on Thursday, but Klopp – whose team face Leicester on Monday – says only the board was responsible.
"Players are not more powerful. We were much more powerful in the past," the German told UK newspapers.
"It depends always on the board. As long as the players talk together there is no problem. If they start talking [to the board] about you, for this you need an ear on the other side.
"It is not about how powerful [players are]. The players need to be powerful but not in sacking managers.
"It's not like the Leicester players did it. It is if someone asked, they gave an answer."
Klopp said maintaining the relationship was straightforward and believes Liverpool proved theirs was in a fine state in January.
Liverpool won just one of nine games in the first month of the year, including slipping out of Premier League title contention and two cups.
"It's not like we come together every day and hug each other. We enjoy the work. I know what they want, they know what I want, so it is very good information," Klopp said.
"We've had some nice moments already and hard moments already and in the hard moments nothing came between us, not in the whole of January."