Both players started in the midweek League Cup win on penalties against Leicester, with De Bruyne scoring his first goal of an injury-blighted season.
The United board are said to be alarmed by Sanchez' comments following Mourinho's sacking.
"When something goes wrong at a football club like this, I think everybody has got to take a wee bit of blame", Bosnich told Omnisport. "Where do you find the players?"
"But the bulk of the responsibility will be shared between the players and the manager".
Jose Mourinho left dropped Paul Pogba right towards the end of his reign
Asked if he could make an impact in his time in charge, Solskjaer replied: "Well, it's six months and I'm going to enjoy the ride".
A host of players from Toby Alderweireld to Harry Maguire, Yerry Mina, Jerome Boateng and Diego Godin were considered by United but were dismissed as either too expensive, or too old, or not being better than what the club already had or a short-term fix.
"Until I get back to football I feel I have the right to live my normal life. A manager of his standing who won two trophies and came second last season to finish on this note was something that nobody was expecting before Christmas".
With Mourinho's departure, Pogba is expected to be reinstated into the starting eleven and the club are hopeful that caretaker manager Ole Gunnar Solskjaer will get more out of the midfielder in the latter half of the season.
"The only thing I can say to you is that it's a surprise for me and not good news, because when one coach finishes his work like that, it's not good for coaches", he said. "Although he's won no trophies, not yet, he might win the EFL Cup", Bosnich added.