I had a similar experience to @thepeopleversuswork, first time around I was too vulnerable and didn't understand how the sites worked or that lots of people are chatting to lots of people and they may just disappear/be in a relationship already/not quite ready for a new relationship/like chatting online but don't want to meet up.
Second time around, I am much wiser to the whole thing, and the second it starts to make me feel negative about myself, I just stop. I find it entertaining more than anything.
Thing is- dating sites are people like yourself! You aren't really ready to date and would probably not want to go through with chatting, then dating, then starting a whole new relationship today, so other people on there may well be the same. The biggest problem with the sites is not married men IMO, there are a few but on the bigger reputable sites they all require photos and most require more than one and quite nice ones to get a response, so that puts the marrieds off- the biggest problem is people who are doing online dating as they are (like you) just separated, or unsure whether to split, or need an ego boost, but really aren't in a position to start a new emotional and physical long term relationship. Others who are then try to match with them and it all ends in tears.
You can't walk into any old bar, glance around for half an hour and then declare there's no-one in there for you ever. How long did it take you to find your previous partner? If it's months or years, that's what it could be like in online dating.
I'd also second the person that said you don't have to go online at all- try MeetUp for groups in your area, including singles ones or hobbies ones or pets ones, or single walking groups, speed dating, there's lots of ways to meet people beyond just hoping for the best.
I would wait a bit til the stress dies down and then read up around how to online date, create a good profile, nice pictures, so you actually stand a good chance of meeting a few nice people. I've met a few, none have been Mr Right, but they weren't sleazy or bad or anything, just nice normal guys! But I don't meet for evening things, or drink or anything on a first date as I don't want to get caught in a situation I don't want to be in, so it's partly how you want to play things- it's all your choice. Including not to online date at all!