Cooper was left exposed by the run of Saints forward Adam Armstrong during the opening exchanges at St. Mary’s Stadium and could only watch as the Newcastle-born striker lifted the ball over Illan Meslier to break the deadlock on the south coast.
Farke admitted during his pre-match press conference ahead of Queens Park Rangers’ visit in midweek that Cooper’s display – along with the rest of the team – was not his best, but one performance will not cause the manager to make sweeping changes to his line-up.
The German is primarily concerned with workload in a Saturday-Tuesday playing schedule and ensuring at-risk members of his squad are not subjected to an increased likelihood of injury by playing too frequently.
Leeds’ boss has rotated personnel in a number of positions already this season, and may do so this coming week when QPR and Bristol City visit Elland Road.
“So far I have to say I'm really happy with Liam. That doesn't mean that he plays each and every second from now on or he starts each and every game,” Farke warned. “But Liam is more like already a Leeds United legend and so important for us.
"He's a natural born leader and he will also be a pretty key player in my squads over the whole season.”
Cooper is into his tenth campaign at Elland Road and has played 269 times for the Whites, many of which have come as club captain. Despite calls from the terraces for Welsh international Joe Rodon to replace the skipper, Farke’s stance towards team selection was a resolute one on Tuesday afternoon.
"Liam is an unbelievably important part of our group there's no doubt, he's our club captain, he didn't win it in the lottery – it's more like it's well deserved.
"If I speak about him as a player and also a human being, [he is] a person who lives [for] this club as more or less, he's got white blood in his veins and I'm full of praise so far.”
As for his most recent performance, Farke acknowledged there was room for improvement, suggesting the club captain will also be held to the same standards as his more junior teammates: “Obviously yes, first goal [versus Southampton], he could have [done better], the last game he was a bit better, but there were three or four little mistakes that led to this goal and when I watch and judge his performances so far, I think he had a brilliant pre-season.
"When he was on the pitch during pre-season, we did not concede one goal, so he was pretty impressive.
"He worked unbelievably hard in the rehab and then he came into the second last game [versus Hull City] after being out for eight weeks in underload, difficult situation and helped us to keep a clean sheet. Then he started against Watford [which] was probably our best game of the season. And again, there was a clean sheet so I'm pretty, pretty happy with him.”
Farke fielded Rodon in Cooper’s absence at the beginning of the season, but after his sending off at the MKM Stadium last month, the 25-year-old Welshman is yet to return to the starting line-up.
"If you want to be successful, you definitely need the core group. I'm not a believer in eleven changes between games,” Farke said on squad rotation.
"For the competition in the squad and also to keep players sharp and fresh if you have options, then to have a few changes – one, two, three – sometimes can be healthy.
"I think he's [Rodon] settled in unbelievable, because he had to play the first games without being prepared without the proper pre-season.
“We had many clean sheets with him, yes also a few games where we have conceded for example, at Ipswich, he was definitely there with good performances but not reached his perfect level.
"I think there's much more to come from him and much more potential for example, when we speak about the yellow-red card [at Hull], he had to handle it a different way, the own goal at Ipswich, there were a few incidents where I would say he can even improve.
“I’m totally convinced of his potential as a player, of his quality as a player, of his quality as a person and this is why I was so greedy to bring him in because I know that he makes us better as a group and we all happy that we have him,” Farke added.