Chelsea swept into an early lead as Tammy Abraham converted Timo Werner's deflected cross – but in the build-up to the opener there were two balls on the pitch at the same time.
Luton were left furious that play was not stopped to remove the second ball, with manager Jones angrily questioning whether the rules had been radically changed without his knowledge.
"Obviously the rules have changed – I asked the referee if it was multi-ball and he couldn't give me an answer," said Jones.
"I'm baffled because I've been in professional football 29 years and in all that time, when a second ball comes on the pitch, play stops. But apparently not today, so I don't know.
"When I approached the referee, he couldn't make eye contact with me, he treated me with the biggest amount of disrespect I've ever been treated with, and just kept quoting the rule book about something I wasn't actually asking him.
"I'm supposed to be wearing a badge today that has 'respect' on it, it's got to be two ways.
"I have respect for everyone I come up against, and today we were shown very little from the referee. And that saddens me."
Chelsea prevailed courtesy of Abraham's hat-trick, with Timo Werner missing a late penalty.
Jordan Clark pegged Chelsea back to 2-1 with a solid strike, but admittedly one that Kepa Arrizabalaga should have kept out.
Jones' ire with Coote was not helped by Luton's tardiness for the start of the second half.
Visiting teams to Chelsea must change in a nearby fitness suite, to comply with Covid-19 social distancing measures.
The lengthy walk to the pitch has caught out a number of teams returning after the half-time interval, with Luton similarly hamstrung.
Coote remonstrated with Luton's players as they zipped through a warm-up, refusing to start the second half.
And Jones insisted afterwards that his players could not have avoided returning late for the second half.
"There's probably a two-minute walk from where we were changing to the pitch, so when the referee blew for half-time it took us two minutes to get back," said Jones.
"Then there's no bell because we're changing in the leisure centre, then we had another two minutes to walk back to the pitch.
"These are strange times, we understand. It's just that instead of the bell going and us being right there, we were two minutes away. So it's just because of the times."