Is It Right To Date My Friend’s Ex?

So Me and this girl have been friends last year on the Same Campus though we kept it lowkey. My friend noticed the girl on campus one day and they proceeded to talking stage. 

My friend showed me the girl and I told him we were just friends I gave him the go ahead. But actually I was interested in the girl but I wanted to study her before making any move. 

So Fastfoward, they dated for a month and broke up. He said he wasn’t interested anymore and I could go for her actually. I’m now close to the girl. I had to let my friend know about it. He said he wasn’t bothered but went behind my back and told my other friends what happened. 

Now all of them think I’m a green snake

Did I do anything wrong?