My computer checkmated me with a pawn move.
I could have taken that pawn en passant but I wasn't given a chance to do that.
Was that a fault of my computer, or is there a rule stating that a pawn giving checkmate cannot be taken en passant?
I would love to see the position; please add it to your question somehow (we can always edit it to look nice). However, there is no such rule. Either your computer doesn't implement captures en passant (improbable these days) or the capture was not valid for some other reason.
Maybe your pawn happened to be pinned?
8/8/7r/5K1k/7p/8/6P1/7R w - - 0 1 1. g4+# hxg3?? 2. Rxh5
As I understand your question, the computer checkmated you with a pawn move from the 2nd to the 4th rank. (Such a move is the only situation that invokes the en passant rule.)
Checkmate ends the game. That is why you were not permitted to capture; the game is already over.