Sunday's clash marked Arne Slot's first competitive game at Anfield, and the Dutchman made just one change to the side that defeated Ipswich on the opening weekend.
With play underway Thomas Frank's side looked to land the first blow against the Reds, and won a corner in the opening stages.
The subsequent delivery was well met by Ibrahima Konate, and the hosts immediately launched into a blitzing counter-attack after Vitaly Janelt failed to dispossess Mo Salah on the edge of the box.
Diogo Jota picked up the loose ball and played in Luis Diaz, who summarily struck home to put the hosts in front on his 100th appearance for the Reds.
Luis Diaz fired Liverpool into an early lead in their clash with Brentford on Sunday
Speaking during the interval Redknapp insisted the German midfielder's failure to be adequately prepared for the potential of Liverpool to break from the corner had cost Brentford dearly.
'Janelt, just keep your eye on him,' the former England international said on Sky Sports.
'He's just not really alive, he's playing with his nose, he starts playing with his shirt.
'He's not thinking "I'm the last line of defense here, this first contact I've got to win", messes with his hair.
'From Brentford's point of view, I just don't see that risk reward, especially a place like here. A lot of teams are trying to do it to condense teams, really make the pitch really small.
'But once that ball comes out, if you don't win that first contact, you got a 60 yard run back to your own goal, you end up in a right mess, just like Brentford did.'
After dominating proceedings following the restart, Salah doubled Liverpool's lead on 70 minutes after latching onto a through ball from Diaz.