Shaw's debut campaign at Old Trafford has been interrupted by persistent injury problems, making 13 Premier League appearances since joining from Southampton for a reported £28 million.
"It's been a frustrating one because of the injuries I've picked up but I’m loving it [at United]," he told Match of the Day magazine.
"If I was to write a school report on my first season here I'd give myself a C-.
"You don't realise just how big Man United is until you're actually here – it’s frightening. It is the biggest club around.
"I’m playing with the likes of Wayne Rooney, [Angel] Di Maria, [Radamel] Falcao and it's weird because my friends always talk about them, saying how good they are and I'm just thinking "Wow, I play with them".
"I'm probably one of the luckiest 19-year-olds to be alive."
United visit leaders Chelsea on Saturday, but Shaw is a doubt with a hamstring problem.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
