Translation:Sorry, we don't have time.
Exactly! However, I do not think that "past tense" is an independent grammar in Chinese. Maybe "我们以前没有空" sounds a little weird to me just as "We were not available" does.
To express the meaning of "before", I believe that you can use "以前", "从前", "之前" or just a single "前". Though in Chinese, the four words sometimes have subtle differences which can even make Chinese native speakers confused. Hope these examples would make some sense:
很久以前，一位王子爱上了一位公主 <-> A prince fell in love with a princess long ago.
从前，一位王子爱上了一位公主 <-> Once upon a time, a prince fell in love with a princess.
在第一次世界大战之前，一位王子爱上了一位公主 <-> Before the World War I, a prince fell in love with a princess.
一百年前，一位王子爱上了一位公主 <-> A prince fell in love with a princess 100 years ago.
对 (duì) = right/correct/to face
不(bù) = not/no
起 (qǐ) = to rise/to be able to
对不起 (duìbùqǐ) = not able to face (lit.) = sorry
Other sorry that we saw:
意 (yì) = idea/meaning/thought/to think
思 (sī) = to think/to consider
意思 (yìsi) = idea/opinion
不好意思 (bùhǎoyìsi) = to feel embarrassed/to find it embarrassing/to be sorry