I believe there is a DL option, but you can only have one or two people on it and they have to actually say "DL" next to their name. Also, keep in mind, you can't make the update until the day after. So, if they go on Tuesday you can't put there until Wednesday I think.
First week has been a bit rough for me too. Victor Martinez went down the first day and has yet to come back. I'm losing this week but I have a pretty solid team, although I would like to make a trade for a decent outfielder
My pitching has been surprisingly great though - just need my offense to pick it up
It's a long season, and all 6 of us are already in the playoffs