The left-back, 23, has been in fine form since the Norwegian took charge at Manchester United.
He has missed just two of Solskjaer's 13 games in charge so far – the wins over Reading in the FA Cup and Brighton in the league.
But despite an impressive record of 11 wins, one draw and one defeat so far and his 'baby-faced assassin' nickname, the boss is determined not to let standards slip and will give a "kick up the backside" when necessary.
Speaking to MUTV, Shaw said: "It’s just amazing to look at the job Ole has done since he came in. How much he has turned it around and how much the place is in a positive way now.
"Ole does it at the right time [shows another side to him]. He knows how good we can be and, if we’re not up to his standards or the standards of Manchester United, he will certainly let you know.
"We’ve had a few moments like that where we might have been comfortable in a game but got a bit sloppy.
"He’s the manager and he tells the players what he wants. It’s good and what we need sometimes, a kick up the backside from the manager, if we’re getting too comfortable.
"It keeps everyone on their toes but he’s an amazing guy and a brilliant manager.”
Like many of his team-mates, the shackles appear to be off Shaw now that Jose Mourinho has left.
The pair had a fractious relationship at times during Mourinho's spell at Old Trafford but Shaw did do enough to earn a new contract in October.
Shaw's performances in recent weeks will no doubt have caught the eye of England manager Gareth Southgate.
He did not go to the World Cup but did start and set up Marcus Rashford in the Nations League game against Spain at Wembley before going off injured.
The defender and his Manchester United team-mates face Liverpool at Old Trafford on Sunday.
And the Red Devils will be desperate to put a major dent in their arch-rivals' Premier League title ambitions.
Shaw added: "This is the biggest and best game to be involved in. Of course, we know how well they’ve been doing and how big the rivalry is between the two clubs. It’s one that everyone wants to be involved in."
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