I would hesitate to read to much into that search statistic. It could be that people were just trying to learn more about the EU once it became huge news the next day. It could be that most of the people searching were people who did not vote either way. It could be that just as many people who voted to remain in the EU also did that search the next day.
I understand the feeling, but still believe that we need to remove barriers to voting, not add more.