That message would appear to be that the Reds are not going anywhere any time soon.
A 2-0 defeat against table-topping Arsenal last weekend cast doubt over Liverpool's ability to compete with the very best and sustain a challenge for Premier League title glory.
They were, however, back to their best at Anfield on Saturday and Skrtel feels they have shown that they have the spirit and ability to push for top honours.
He told Sky Sports: "We wanted to send a message - we are here and we are ready to fight. We are happy with the three points today.
"We wanted to keep a high tempo. Even after the first half and it was 3-0, we wanted to play our game."
Skrtel was among those to get in on the act against Fulham, as he nodded home a Steven Gerrard corner to put Liverpool two goals to the good.
He said of his 10th goal for the club: "It was a brilliant cross. I have scored 10 goals and maybe three quarters of them have been from a pass from Stevie.
"I'm happy because that was my first goal (of the season) and hopefully I can get a few more in the future."
Next up for Liverpool, after the international break, is a derby date with Everton, but Skrtel insists the Reds will not be placing added importance on another potentially tricky test.
He added: "That is a big game but for us now, every single game is a big game in every competition.
"We want to be up at the top and we will fight for the league. Every single game is big for us."