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Garner's Modern American Usage (p705) has an entry on the two words:

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

So you need regrettably in your example:

Regrettably, she could not see her father for the last time.

Regrettably, she could not see her father for the last time.

Regretfully is less likely to start a sentence. A possible example is:

Regretfully she admitted to having been unkind to her father the last time she saw him.

Regretfully she admitted to having been unkind to her father the last time she saw him.

Garner's Modern American Usage (p705) has an entry on the two words:

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

So you need regrettably in your example:

Regrettably, she could not see her father for the last time.

Regretfully is less likely to start a sentence. A possible example is:

Regretfully she admitted to having been unkind to her father the last time she saw him.

Garner's Modern American Usage (p705) has an entry on the two words:

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

So you need regrettably in your example:

Regrettably, she could not see her father for the last time.

Regretfully is less likely to start a sentence. A possible example is:

Regretfully she admitted to having been unkind to her father the last time she saw him.

2 added 72 characters in body
source | link

Garner's Modern American Usage (p705) has an entry on the two words:

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

So you need regrettably in your example:

Regrettably, she could not see her father for the last time.

In other words, she regretted that she could not see her father. This made her feel regretfulRegretfully is less likely to start a sentence. A possible example is:

Regretfully she admitted to having been unkind to her father the last time she saw him.

Garner's Modern American Usage (p705) has an entry on the two words:

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

So you need regrettably in your example:

Regrettably, she could not see her father for the last time.

In other words, she regretted that she could not see her father. This made her feel regretful.

Garner's Modern American Usage (p705) has an entry on the two words:

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

So you need regrettably in your example:

Regrettably, she could not see her father for the last time.

Regretfully is less likely to start a sentence. A possible example is:

Regretfully she admitted to having been unkind to her father the last time she saw him.

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source | link

Garner's Modern American Usage (p705) has an entry on the two words:

Errors made are regrettable; the people who made them should be regretful. The most common error is to misuse regretful for regrettable, particularly in the adverbial forms.

So you need regrettably in your example:

Regrettably, she could not see her father for the last time.

In other words, she regretted that she could not see her father. This made her feel regretful.