It could pose roughly two different meanings depending on the context. For example: 졌잖아 could mean past tense of 'losing'='지다' and '잖아' used to ask for agreement or blaming. (e.g. 너 때문에 졌잖아. = I lost because of you.) 졌잖아 could also mean a past tense of 'become' and describe a present state of being. For example, '우리가 헤어진 뒤로 너는 괜찮아 졌잖아' = 'You became fine/okay after we broke up.' Here, 잖아 can mean two different things depending on context, and basically whether if '잖아' was used in a statement or a question. For instance, '잖아' in a statement often used to blame things on someone or to express his/her opinion that things happened because of someone or something. However, if '잖아?' is used in a question like so, it pretty much simply asking for an agreement. Rough translations for '잖아 (안그래)?' in a question would be '(it's okay,) isn't it? / (you are fine), aren't you?' Disclaimer: I do not have any linguistic degrees or certificate for the Korean language, but my answers/suggestions are based on my expereinces as a native speaker.

The speaker supposes that the listener knows also the fact he is referring to.

Depending on the context it could mean: you know I lost. you know you lost you know he lost...etc