Most people voted for Brexit to stop immigrants "taking their jobs", and to try and piss off useless UK politicians. They might tell themselves after the fact it was for some other reason now they realise what they have done.
I've never heard anyone say they think their vote "matters more" because of Brexit. Aside from the fact it is patently untrue (we still use the least democratic and most divisive method, FPTP) the EU Parliament elections are actually more democratic by virtue using PR, which allowed UKIP to send a load of MEPs to Brussels.
More than a smaller party could ever get into Westminster even if they had a similar proportion of support due to our broken democracy.