Biz başka severdik o yüzden başka sevemedik...

tesekkur ederim

 we used to love another therefore we couldn`t love another

my try

 there is a play on words here, so that would be ;

We used to love eachother in such a unique way, therefore we couldnt love someone else.

"başka" in this case is " in different way, in such a unique way, very different from others "

so these people had a special love for one another , and after they split up or left one another they couldnt love other [baska] .

so in the second sentence "baska" means " other " [someone else]

I hate play on wordsjust say it as it is

As Turks we like play on words Sorry

Some more examples ;

A dog not only has a fur coat but also pants

I work as a baker because I knead dough

What is the difference between a conductor and a teacher?

The conductor minds the train and a teacher trains the mind.

I used to be twins. My mother has a picture of me when I was two