Brendan Rodgers's side is still in the second tier when it comes to striking deals for the best players around, and won't be able to land a replacement for Suarez.
He said it when Luis Suarez's transfer to Barcelona was confirmed and again when the Reds pulled the plug on Loic Remy's move to Anfield over a supposed problem with his medical.
Yet there are signs that the opposite might be the case behind closed doors at the Merseyside club.
In the last week, Liverpool has made attempts to sign Ligue 1 stars Radamel Falcao and Edinson Cavani.
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The club's ambition to even consider signing two of the most coveted strikers on the planet is commendable, but in reality they have no chance of signing either player.
Liverpool may have returned to the Champions League this season, but the club has realized this week that it does not mean the team can now shop in Harrods.
The signings Liverpool has made this season shows very much that the Reds are still in the second tier when it comes to the transfer market.
All of the players who have arrived at Anfield would have done so regardless of their Champions League qualification, especially given Liverpool's global status and significant riches.
The pool of players in which Liverpool is shopping can strengthen the squad significantly as they prepare to fight on several fronts while mounting another title challenge after last season's second-placed finish.
But the club won’t be able to replace Suarez.
Tottenham could not replace Gareth Bale, Arsenal could not replace Robin van Persie, and Liverpool will not be able to replace Suarez.
How can you? It was not just his 31 goals that made Suarez so electrifying last season. His leadership, flair, audacity and sheer will to win all need to be replaced, too.
Rodgers has been bullish when asked whether Liverpool risks repeating the considerable mistakes made by Tottenham when the club sold Gareth Bale last summer.
"It's a different club and different vision we have here. At Liverpool there's a strategy behind what we are doing," he said.
The moves for Falcao and Cavani suggest, though, that the strategy includes buying a star name to replace the hole left by Suarez and to lead the attack.
Alexis Sanchez would have been perfect but he turned down Liverpool to move to Arsenal.
Now the Reds are looking at audacious moves for players who are either out of their price range or beyond their pull of attraction. The whole world knows that, if Falcao leaves Monaco, his most likely destination is Real Madrid. It's unrealistic.
If Liverpool can land a big-name attacker, it will give the club a huge boost ahead of the new campaign, but the team is finding out just how hard it is to replace special players.
EVERTON WELL-EQUIPPED FOR TOP-FOUR ASSAULT
On the other side of Stanley Park, it has been a very good summer so far for Everton as the Toffees look to build on last season's fifth-placed finish.
After his 15 Premier League goals last summer, Everton has spent 35 million euros to sign Romelu Lukaku from Chelsea on a permanent deal.
He is joined by another player who starred on loan last season, Gareth Barry, while Bosnian midfielder Muhamed Besic has arrived in a €5 million deal.
Just as importantly, John Stones and Ross Barkley have signed new contracts amid interest from rival clubs.
The two players are already key components of Martinez's squad and are bound to become future stars.
It means Everton has kept the core of its squad, while you can trust that Martinez will be on the lookout for some more clever loan deals towards the end of August.
David Moyes always suffered at Goodison Park because his best players were sold after impressive performances.
Everton has kept the vultures away - at least for now - and is well placed for another attempt to break into the top four.