The Norwegian won 14 of 19 matches while in charge of the Red Devils as caretaker, but since his appointment on a permanent basis last month, United have lost four of six.
Sunday’s 4-0 rout at Everton was a new low, with many critics calling it Manchester United’s worst performance since Sir Alex Ferguson’s retirement.
Nonetheless, Solskjaer remains confident.
Asked if he could turn United back around, Solskjaer said: “I would like to to say yes.
“It’s not down to me to say that but I’m confident in my team and I’m ready to take on the challenge.