The Red Devils suffered a humiliating 6-1 defeat at the hands of Spurs on Sunday, which leaves them 16th in the Premier League table after only three matches of the 2020-21 campaign.
United were equally poor against Tottenham, who dominated proceedings at Old Trafford after falling behind to a second-minute Bruno Fernandes penalty.
Son Heung-min and Harry Kane each grabbed a brace for the visitors, with Tanguy Ndombele and Serge Aurier also getting in on the act to make it a happy return to Manchester for Jose Mourinho.
The Portuguese boss coached the Red Devils between 2016 and 2018, but ended up being sacked amid reports of a fractious relationship with several members of the first-team squad.
Keane thinks certain players were guilty of not giving their all for Mourinho, and that history is now repeating itself with Solskjaer at the helm.
The United legend can't see the Norwegian lasting much longer in the managerial hot seat, as he told ITV Sport: "The performance against Spurs was disgraceful.
"We’ve all be in football, we’ve had bad days but I thought it was a disgrace to the badge some of the players’ performance. Too many bluffers.
"Ultimately, I think it will cost Ole his job. With the players he’s got there.
"I’ve said it before, they threw the previous manager [Mourinho] under the bus and they’ll do exactly the same to Ole."
The international break has given Solskjaer extra time to reflect on the weekend's event, with the majority of his senior squad currently away on international duty.
Preparations for a crucial away fixture against Newcastle on October 17 will begin next week, and a couple of new faces could be in line to feature.
United managed to bring in Alex Telles from Porto and ex-Paris Saint-Germain star Edinson Cavani on a free transfer before the summer market closed on Monday, with both men likely to be available to make their debuts at St James' Park.
The Red Devils are due to open their latest European campaign against PSG at Parc des Princes three days later, as the Champions League kicks off again behind closed doors.