Keane, however, has insisted that the Reds have only been beating the "lesser teams", and the 46-year-old has insisted that there will be 'big tests to come' for Jurgen Klopp's side.
"A comfortable night for them tonight, a good start and their attacking players certainly enjoyed it. But the big tests are yet to come for Liverpool," Keane told ITV.
"Clearly they're beating these so-called lesser teams, and the same in the Premier League. But they've beaten nobody domestically and in Europe yet."
Liverpool have won seven of their last nine games in all competitions, and will look to continue their run of impressive form when they welcome Everton to Anfield for the Merseyside derby on Sunday afternoon.