The Owls ended a seven-game losing streak thanks to Chris O'Grady's first-half strike, which was shrouded in controversy after Gary Madine appeared to foul Barnsley goalkeeper Luke Steele in the build-up.
Jones, whose position has been under increasing scrutiny, admitted he was relieved to benefit from a slice of good fortune but still took a swipe at referee Stuart Attwell.
"It was ugly but well earned," Jones said of the win. "We had Lady Luck on our side for a change, but we deserved it because we battled hard.
"Gary has admitted that he has barged the goalkeeper, we have not had that luck but today it was our time.
"We got the break today, last week we battered Bristol City and didn't get the break.
"But I thought the referee had an absolute shocker to be fair. Everything after that went against us and he struggled to keep control."
Jones insists spirits in the camp have remained high during a barren run, but admits he hopes the result will serve as a wake-up call to several members of his squad.
"There is a good feeling in the camp," he added. "We were scratching our heads as to why the run had been that long, but they all did their jobs and when they don't lose their concentration they are capable of getting a result.
"It just proves to certain individuals that if they listen and want to do it then they can. It's a dig at certain individuals but today everyone concentrated."