United’s record signing Rhian Brewster put the Blades ahead before Jack Robinson headed his first goal for the club to seal a happy homecoming for Paul Heckingbottom’s men, who were playing their first game at home for 55 days after a spate of postponements during December and January.
Luton were also reduced to 10 men in the second half when Reece Burke saw red for dragging back Brewster as he looked to race onto Ollie Norwood’s excellent pass and bear down on goal.
And Jones admitted: “We have to be at our best to beat these.
“They were in the Premier League last year under Chris [Wilder] and came out of the traps in the second half, and we didn’t handle that.
“In the first half we matched arguably the best squad in the Championship. Norwood is a serial promotion winner, [Iliman] Ndiaye I really like, Billy Sharp has been there and done it and they paid £20m for Brewster.
“We’ve not spent £20m in our history.”
Town thought they had gone ahead when Sonny Bradley headed in a free-kick, but it was ruled out for offside – with Jones having few complaints about the “marginal” decision.
“The Championship is relentless and this is a difficult place to come,” he added.
“So for us to come here and do what we normally do to teams is a big ask, and that was the case today.”