Whatever happens next in politics, there will be cuts to the cultural sector. The arts might be amazingly valuable to this country, but politicians know that artists are a minority, and an endangered minority. Very few people are going to bleat loudly if highbrow entertainment gets a bit of a pinch.

In the runup to the election, there was little talk about the arts. I read an interview with Chris Smith, the former culture secretary, and he put it down to the fact that people such as Alastair Campbell thought real people watched football and went to pop concerts. When politicians use the word "real", they usually mean depressingly average, sentimental, bitter and anti-intellectual types.

Arts organisations will, of course, respond to these threatening cuts. I was recently at an event at the British Museum – the Cultural Capital campaign – and lined up on the stage were all the panjandrums of high culture: Nicholas Serota, Neil MacGregor, Jude Kelly, Nicholas Hytner, Alan Davey, head of Arts Council England. They spoke about how important the creative industries are to the economy: it's estimated at 8% of GDP, an incredible amount when you think how few people are employed in it. But I had a suspicion that they were like the glamorous lost leaders of UK Culture PLC, and that the real money is now made by computer game designers, high street fashion and – dare I say it – Top Gear doing well in Poland.

We all care about the quality of our culture, but are the tears shed at an opera any better than those shed at a football match? Are they better quality tears? People sometimes talk as if there is a vintage type of tear that is shed only at Glyndebourne.

Throughout my career, I have suffered terribly from what I would call "impostor syndrome". I grew up in what used to be called a working-class household. I tried to think of a politically correct equivalent, and I came up with "people of restricted taste". We didn't have classical music on in the house; it wasn't for the likes of us. I still feel, when I'm listening to classical music (and I like it a lot), as if I'm pretending. It's worse when I go to the theatre, where I feel as if I've wandered into a particularly middle-class drawing room with a game of charades going on. I want to stand up and say: "Stop pretending!"

I understand the efforts of cultural institutions to attract a wider audience, because the visual arts have been through a very similar game. When I started out as an artist 30 years ago, it seemed a very rarefied, obscure activity. I got into it because I liked drawing, really. But I climbed the greasy pole, and I was a little bit cheesed-off, when I finally got up into the middle-class stratosphere of the art world, that it had suddenly decided to go all accessible. Galleries were full of school parties, baby buggies, people taking photographs with their phones – democratising art. Perhaps it is churlish of me to complain, when I have benefited from the popularity of contemporary art. Class travellers can be the worst kind of snobs.

Classical music has gone through a similar sort of transition. It's let its accent slip, it's put on a bit of lipstick, dabbed on some hair gel. But a word of advice, classical musicians: avoid the c-word. Cool is a word that often crops up when it comes to talking about art, and it's always bugged me. Being creative is all about being unselfconscious; being prepared to make a bit of a fool of myself. In my experience, embarrassment is not fatal.

Few groups are straighter or more conservative than teenagers, who take cool seriously. And what makes cool very immature in my book is that it's a binary judgment: hip v square; in v out. The other week, I quizzed my 15-year-old neighbour about what the current words for "cool" were. He told me that cool can be "sick" or "nang", and uncool is "wack". Or interestingly, considering the attention span of the modern youth, uncool can be "long". As in: "Man, that opera was long."

I'd like to make a plea for difficulty over cool. In the end, I think being difficult is the coolest thing you can be. One of my guiding principles in life has been to follow the path of most resistance: as soon as I start doing something well, I get bored. So I try to do something a bit harder.

When I listen to a piece of classical music, what makes me well up is not just the melody, or the musicians' interpretation, it is the thought of the thousands and thousands of hours of practice. I'm in awe of the rigour, the dedication. Musicians seem to have a much clearer sense of what they're aiming for. In art nowadays, there's a terrible sense that anything goes – it makes me a bit sad. Musicians must continue to make difficult work, music that I can aspire to understand – and do it for the love of it. Here in the arts, we have to set a good example.

This is an edited extract from a lecture given at the Royal Philharmonic Society Music Awards on Tuesday. For the full text and details of the winners, go to rpsmusicawards.com