Manchester United bowed out of the FA Cup after a penalty shootout against Middlesbrough on Friday night.
Earlier in the week, Lingard came out on social media to explain his absence and said it was advised by the club for personal reasons.
Cavani had been playing in South America for Uruguay on international duty and he would not have been able to train and be ready for the match.
Rangnick wanted Lingard to play
The German said: "With Jesse, I told you what my information was and my knowledge was, and of course, I would have loved to have had Jesse in the squad.
"We were one outfield player less on the teamsheet today, so why would I have allowed him to have four or five days off?
"I would have loved to have had him in the squad but it was not the case and therefore, it doesn't make sense to speak about players who were not available," the United interim said.
On Cavani he reiterated the fact the Uruguayan striker would not have been able to play in the dull FA Cup affair.
"No, because he played for Uruguay on Wednesday (morning). With jet lag and the travel arrangements, it would not have made sense. He wouldn't have been in the squad anyway."
30 shots, nine of which were on target but it was not enough to get past Joe Lumley. He stood tall in between the sticks and United got what they deserved as they crashed out on penalties in dramatic style.
The young Swedish forward, Anthony Elanga, fired the decisive penalty over the bar and United are headed towards their sixth season without a trophy.