Unfortunately, SequenceMatrix won't let you concatenate unaligned sequences -- we didn't want someone spending all afternoon carefully concatenating all your sequences before realizing that there weren't aligned, making them useless for downstream analysis!
Of course, you don't have to align the sequences -- you could pad the end of the sequence with 'N's or '-'s (gaps) so that they're all the same length, but this will make downstream analysis harder, if not impossible. If you want a quick-and-dirty way of doing this, one technique I know is to individually import your files into Species Identifier (
http://gaurav.github.io/taxondna) and then exporting them as Nexus from there, which will pad the ends of your sequences with gaps. You will have to do this with each input file individually, which might be okay if you don't have too many of them. If you do, you'll need to use some other tool to do this -- I don't know if SeqBuddy (
https://github.com/biologyguy/BuddySuite/wiki/SeqBuddy) or one of the other tools in that suite can do that, but if not, you should get in touch with its creator and let him know that this is a feature you'd like!