在写留学英语邮件表示遗憾时，可以使用以下表达方式和句子：

Subject: Re: [主题]

例如：“Subject: Re: Budgets”

开头问候

例如：“Dear [收件人姓名],”

表达遗憾

例如：“I regret to inform you that…”

例如：“I'm very sorry that…”

例如：“Unfortunately, we regret to say that…”

说明遗憾的原因

例如：“due to unforeseen circumstances”

例如：“because of a delay in our process”

提出解决方案或补救措施

例如：“We will do our best to rectify the situation.”

例如：“Please let us know if there is anything we can do to assist you.”

结束语

例如：“Thank you for your understanding.”

例如：“Best regards,”

示例邮件

Subject: Re: Budgets

Dear Ted,

Thank you for submitting next year's preliminary budget. I regret to inform you that we will not be able to accommodate the additional expenses you requested. Due to unforeseen circumstances, our budget has been tightened, and we must prioritize our spending.

We understand the importance of your project and will do our best to find a solution that works for both parties. Please let us know if there is anything we can do to assist you or if you have any alternative suggestions.

Thank you for your understanding.

Best regards,

[你的名字]

通过以上步骤和示例，你可以有效地表达留学英语邮件中的遗憾情绪，并确保邮件内容清晰、礼貌且具有建设性。