From Multi-Lex:

ему жаль куска хлеба — he grudges a bit of bread
As a native American English speaker, I find this example very "weird-sounding" -- nowadays, "grudge" is quite often used as a noun (as in the horror movie The Grudge), but rather rarely used as a verb.

Instead, the prefixed form "to begrudge" is the more commonly used verb form, and is especially common as a negated verb:

I did not begrudge him the food. (I did not regret giving him the food; I did not mind parting with the food.)
I don't begrudge the time I spent learning Latin. (I don't consider it a waste of time, although I've mostly forgotten my Latin.)

If you want to express the opposite meaning (that you were unhappy to part with the food), you can say EITHER:

I begrudged him the food.
I begrudged the lost time.

...OR you can use the adverbial form "begrudgingly", modifying a verb such as "to give" or "to part with" or "to lend", etc.":

I begrudgingly gave him the food.
I begrudgingly lent him the five dollars.
I spent the time begrudgingly.

In my opinion, the negative "to not begrudge" and the positive adverbial construction "to begrudgingly give" (or "to begrudgingly part with", etc.) sound especially natural and colloquial -- more so than the positive "to begrudge", and MUCH MUCH more natural than "to grudge."

PS. Let me repeat that I'm a US English speaker -- it's possible that UK speakers would totally disagree with me.

PPS. The non-prefixed adjective "grudging" and the adverb "grudgingly" are also in common use, and are synonyms for "begrudging" and "begrudgingly". However, there is no such noun as "begrudge" -- you can say "He had a strong grudge", but "He had a strong begrudge" is impossible!