No we shouldn't. The BBC doesn't fund the contest directly, it pays an annual membership fee to the European Broadcasting Union. The amount of that fee is also determined by the size and population of the country. It's also cheaper to send an act to Eurovision than it is to produce one episode of The Voice or Strictly Come Dancing.
Lest we forget the UK finished 5th in the public vote in 2011 with Blue, and 5th overall in 2009 with Jade Ewen. The UK does have the ability to do well, it's just that the BBC doesn't seem to recognise what type of songs succeed in Eurovision these days.
Another thing that has to change is the public's perception of the contest. Thanks to years of Terry Wogan everyone seems to think the voting is political. It's not. There is Cultural Voting which exists. Of course Norway will vote for Sweden as the Swedish song has probably been played to death on their radio station, and vice versa.
The BBC does need to take the contest a bit more seriously, this is the main criticism of other countries towards the UK. I would be in favour of scrapping the Big 5 rule (where France, Germany, Spain, Italy and the UK automatically qualify) and make everyone go through the semi finals. This would result in these countries sending better quality songs.