Arsene Wenger made the bold decision to drop star forward Alexis Sanchez for Saturday's trip to Anfield, but Arsenal went into the interval two goals down as Roberto Firmino and Sadio Mane scored for Jurgen Klopp's hosts.
Wenger brought Sanchez on at half-time and the Chilean duly set up Danny Welbeck to give the Gunners hope, but Liverpool secured the victory as Georginio Wijnaldum swept home a late move in injury time as the Reds leapfrogged Arsenal into fourth.
Arsenal face a huge battle to qualify for the Champions League next season with Manchester United just a point behind them in sixth, while league leaders Chelsea now sit 13 points ahead of their London rivals with 12 games remaining.
Goalkeeper Cech says the Gunners must readjust their aims as their hopes of lifting a first league title since 2004 disappeared once again, telling BBC Sport: "We were more aggressive after the break and started winning the 50-50 battles.
"It's disappointing when you lose the game, but more disappointing conceding the first two goals because we weren't in danger.
"With three points we would have been in the chase for the title, but now we're too far.
"We need to ensure that we finish as high as possible and in the top four."