Solskjaer has faced continuing scepticism at Old Trafford ever since his permanent appointment as manager in March.
But Shaw was quick to defend his manager when asked whether he felt the club was going in the right direction.
"Of course," he told the official Man Utd website. "I feel that the squad we have is no different from the squads that are challenging for the title."
"We've got such amazing players and some amazing young players who are still learning. Of course, we're all still learning and all still wanting to improve.
"Everyone at this club wants the best thing for this club and even more so from the management side.
"We've got great coaches and a great manager, that knows this club inside out. He knows what is needs to bring the good old days back that he once had under Sir Alex [Ferguson]."