Mourinho agreed, saying: "Exactly, (it) is a collective thing, the reason why we don't win is responsibility of everybody".
"Whether it's the best or the worst moment to play them, who knows?"
The selection gamble contributed to United being picked apart easily by a West Ham side with only one win from its previous six league games.
Mourinho told Carragher after his Stamford Bridge departure that he had learned not to overly criticise a player in front of his teammates. "He has got nowhere near the levels we saw at Arsenal since the move and you have to ask why".
Mourinho's public spat with star midfielder Paul Pogba has been another sideshow to a stuttering season.
"A Champions League week is always a good week, even if you expect a hard match, a hard opponent", Mourinho said.
'He (Shaw) says "we players are on the pitch, we have to perform, we have to give more".
Jose Mourinho: Some Manchester United players care more than others
United won their opening game in the Champions League last month against Young Boys and another victory will boost their hopes of qualifying for the knockout stages.
Mourinho was also quizzed about a report which claimed he was already preparing for his Old Trafford exit after receiving a call from Zidane, the favourite to replace him.
Rio Ferdinand, the former Manchester United defender, says the club have "big decisions" to make in the coming weeks.
According to reports, Mourinho criticised Sanchez in a team meeting at the start of last week, as well as two other senior players. "I look in the mirror and see where I can do better".
The 30-year-old was prevented from being asked about the feeling around this squad compared to the one that fell out with Mourinho towards the end of his second spell at Stamford Bridge. "I see different actions but what you see is not really inside".
Unlike numerous other top players in the Premier League, Sanchez enjoyed a summer off as Chile failed to qualify for the World Cup and was tipped to have a big impact at Old Trafford this year.
Luke Shaw was willing to talk about his side's performance on Saturday saying, "We didn't look like a team today that was going to beat West Ham".