The ex-Liverpool skipper, who won seven titles and three European Cups between 1971 and 1984, has labelled the recent wretched run unacceptable.
Thommo, 58, said: "Since the Carling Cup and prior to the Carling Cup, it has not been good enough.
"Everyone has to take responsibility for the results - the players, Kenny and his coaching staff. Everybody.
"But there's no question Kenny is the right person for the job."