Weimann struck an equaliser for the visitors before Santi Cazorla's late Arsenal winner.
He told Villa's website: "It was brilliant to score the equaliser and we tried to see it through. But it was my fault for the second goal because I let the full-back cross it in. I was very disappointed.
"I thought we played brilliantly overall. The whole team worked hard and every time we broke forward we looked like scoring. The defence was brilliant.
"But in the end, we switched off for one second and they scored. It shows you that you can't switch off, even for one second. These sorts of teams are good at using that and scoring against you.
"Arsenal are a brilliant team, even though they haven't performed brilliantly for the last couple of weeks. The players they have are outstanding.
"But I thought we played really well. It was just that one moment where we switched. But now we need to move on."