Behind whom?

I mean, I get it, my own country is doing badly even compared to other EU countries but we need to keep in mind that the EU is at 10% or so vaccinated which is a lot more than almost any other major country or political bloc.

If you show only the UK and US as comparators, it looks really bad but that's a hard comparison set to go up against.

It's actually really ironic that the the UK and US took an approach that most people would consider a very European one by directly involving themselves and investing up-front in vaccine production while the European Commission took the neoliberal route of placing commercial orders in most cases and doing some but much less direct investment.

What has ended up happening is basically the confluence of suboptimal but not necessarily bad decision making and some really bad luck.

The EU, UK, and US all bought large portfolios of vaccines, enough a few times over if they all worked. They also all invested up-front in R&D, the EU proportionally less per head of population but of course many EU countries are not so rich and do not have so much domestic biotech/pharma so this has to be seen in that context as well. The EU is not all France/Benelux/Germany which do have such industries.

All three gambled that their portfolios would pay off.

US went heavy on J&J, Pfizer/Biontech, Moderna (not as sure about the US portfolio but loads of others)
UK went for AZ, Valneva, GSK/Sanofi, Novavax, Pfizer/Biontech, (and later bought some Moderna but not much and only after it was approved). There is some kind of future agreement with CureVac which was only recently concluded.
EU went for Pfizer-Biontech, AZ, J&J GSK/Sanofi, CureVac, Moderna. I think there have been discussions with Novavax and Valneva but no concrete orders.

(UK and EU have the vaccines roughly in order of order size)

So what happened?

Essentially the Pfizer vaccine worked brilliantly and they seem to have gotten their scale-up working quite well. Good for EU and UK both.

AZ works well (probably slightly less well, and with quite a lot of evidence that the decision not to use the stabilised fusion protein is what is making a difference to performance against certain variants) but AZ is having an absolute nightmare getting their yields up. This has affected all their global production - they had intended to delivery 30m doses to the UK by September... 2020 and 100m by the end of the year and clearly have not been able to. Making biological products is really hard, clearly. This has slowed down both the UK and EU roll-outs but because the UK scale-up started earlier (note my comments above about investment agreements, they started production scaling at their Oxford site as early as April 2020) they are further in the production ramp and of course most of the UK delay was before the vaccine was approved. So despite their UK order technically being later than their EU order, it has been felt much harder in the EU because the "lateness" of the UK order mostly happened before the vaccine (or any other vaccine) was approved.

The GSK/Sanofi vaccine has been postponed and may never see the light of day.

Novavax has had good results and is currently preparing for the approval process.

Both the UK and EU had hoped to use either AZ or GSK/Sanofi as their "workhorse" vaccine but the UK had slightly less emphasis on it and bought / invested in more doses of vaccine per head. The EU has not done a great job here but it's also not abject failure, they've just had some bad luck in that simultaneously their two biggest orders were cancelled and slowed down.

It could easily have been the case that a different set of vaccines didn't work and/or were hard to make and then it might be the US or the UK with the problem.

I think before we draw big picture conclusions (apart from Ursula vdL being useless, but I think any German who remembered how good she was at defence procurement could have told you that) we need to remember that to some extent there are historical contingencies at play here and we can end up over-fitting by assuming that literally every difference we see is due to structural problems/advantages faced by one side or another.