Brendan Rodgers is the fourth manager the Slovakian has played under during his near six years at Anfield, with the boss navigating his second season at the helm.
With the Northern Irishman's summer signings also adapting quickly to their new environment in his opinion, the centre-back was in a positive humour after finding the net in a 4-0 victory over Fulham.
He told Liverpoolfc.com: "Of course, it's always nice to score goals. But the most important thing was to get three points. We got them and we're happy with that.
"It's very important to get a good start to the season and we want to carry on this way. The new players we signed in the summer have settled into the team well.
"We are in the second year with the manager and the same group of players for two years - we can see it is working, and I hope it is going to work in the future as well."
After Fernando Amorebieta had diverted a Steven Gerrard set-piece into his own net, Skrtel slammed a header from another delivery by the captain past the static away defence.
The 28-year-old's effort provided the platform for Luis Suarez's double to add gloss to a satisfying triumph, particularly with a first clean sheet for Rodgers' side since September 1.
"It's always nice for the defenders to get a clean sheet, because it has been a few games since we did," said Skrtel.
"We said after the first half it was very important to try to get a clean sheet. We got it and I'm happy about that as well.
"It was a great performance from every single player in the game, attacking or defending. Those types of games are very difficult for your focus and concentration, because maybe as a defender you don't have too much work to do but you have to be focused.
"There are always dangerous players - Berbatov, Kasami or Ruiz. It wasn't easy, but we absolutely dominated the game and scored four nice goals. We fully deserved three points."
After electing for a 3-5-2 formation for the previous six matches, Rodgers reverted to a 4-3-3 system for Saturday's clash.
From an individual point of view, Skrtel believes the change has little impact on his task at hand; however, the No.37 explained why it is a beneficial alternative for Liverpool moving forward.
He added: "It's not a massive difference if you play two or three centre-backs. You have to do the same as a centre-back - try to not let the striker score. It's not a big difference.
"In the last few games we played with three centre-backs and it was working well. And it was the same today. It's good for the team if we can switch from one system to another."