Lapthorne, the third seed, was playing Australian world number one Dylan Alcott, with whom he won the doubles event 24 hours earlier.
Alcott, a 12-time grand-slam winner, said after that match that he was hoping to "smoke" his partner and he did just that, winning 6-0 6-2 on Court 12.
Two-time Paralympic silver medallist Lapthorne was staring at a dreaded double-bagel at 6-0 5-0, but he managed to get two games on the board before Alcott wrapped up victory.
An emotional Lapthorne said on court: "I'm trying not to do an Andy Murray! Hopefully I can come back next year and put on a better show.
"Congratulations to Dylan, thanks for yesterday, he was far too good today. If he's on it like that and I'm not, that's what happens."
Alcott, who is also a radio broadcaster in Australia, said: "As you can see I love talking on the court as well.
"Big thanks to Andy. You're an absolute legend, I loved winning the doubles with you yesterday, and you're a great bloke.
"To come out at Wimbledon and get to play on the grass, for a kid who grew up in a wheelchair, it was a dream come true for me.
"And to all my friends who have come to watch, let's get absolutely sauced tonight."
Quad wheelchair tennis was making its competitive debut at Wimbledon having appeared as an exhibition event last year.
Lapthorne will take home £17,000 as runner-up with Alcott pocketing £34,000.
There was more British disappointment in the men's wheelchair doubles final with three-time winners Alfie Hewett and Gordon Reid beaten 6-4 6-2 by Joachim Gerard and Stefan Olsson.