After two Charlie Hodgson penalties, London Welsh scored the first try of the game through new addition from Harlequins Seb Stegmann to make it 6-5 after 26 minutes.
A penalty try in the first half was followed by scores from Joel Tomkins and Will Fraser in a 15-minute spell in the second half before David Strettle added the fourth late on.
Hodgson recorded 15 points from the boot in total with Henson contributing two penalties and a drop goal to London Welsh's score at Allianz Park.
Three points separate the Exiles and bottom club Sale Sharks in the Aviva Premiership table and head coach Jones was a far from happy man after their 13th defeat of the season.
"Coaches, players or anybody involved in rugby aren't perfect; we all mistakes but all we ask for is consistency and that was missed," said Jones, who saw Phil MacKenzie and Tom Bristow yellow carded in the first half.
"You just want to go from week to week with a basic understanding of what is a competitive ruck. I felt the first two rucks were clear wins for us but they were penalties against us and if that's what the rules are that's fine.
"But then in the second half it wasn't like that - are you allowed to compete for the ball or not? I'm just confused about it and I'm just a coach.
"I don't know what it's like for players because one week it's all one thing then the following week it's completely different and I'm struggling with the consistency."
Meanwhile, if England head coach Stuart Lancaster came knocking then Tom Croft would answer his call with aplomb according to Leicester Tigers director of rugby Richard Cockerill after the flanker continued his comeback from a broken neck.
Croft was stand-in captain for the visit of bottom side Sale and played the full 80 minutes as doubles from Matt Smith and Ed Slater, a penalty try and a Mathew Tait effort lifted the Tigers to a 48-10 victory.
And Cockerill has seen enough to say with confidence that the 27-year-old is ready to contribute straight away to England's remaining Six Nations campaign.
"He is a good enough player to go and play," he said. "He has played two full games now and if England needed him I'm sure he would be ready to go and do a job.
"Tom's attitude has been outstanding and he has used the time when he has not been playing to deal with his contact work and his conditioning.
"With 15 minutes to go he was wanting a bit of oxygen but he works to the maximum all the time. I'd have no hesitation in saying that Tom is ready to go and play a Test match next week.
"He has worked really hard and been patient and we are now getting the rewards."
Elsewhere on Saturday, Northampton Saints wing Jamie Elliott followed up with his double against Bath Rugby by going one better in a 40-14 win over London Irish at Franklin's Gardens.
Elliott was joined on the scoresheet by Soane Tonga'uiha and Samu Manoa as Stephen Myler added four conversions, the Exiles' points coming from a Guy Armitage try and three Tom Homer penalties.
And Exeter Chiefs recorded a first-ever Aviva Premiership double over Harlequins as they left the Stoop 27-16 victors.
Ugo Monye had put the defending champions ahead after just five minutes but second-half tries from Damian Welch and Luke Arscott reignited the Chiefs' Heineken Cup charge.
On Friday night, Jonny Arr's try 12 minutes from time sealed a vital bonus-point 29-23 victory for Worcester Warriors, condemning London Wasps to a second successive defeat in the process.
And Bath Rugby earned the local bragging rights after winning the West Country derby with Gloucester Rugby 31-25 at the Rec thanks to tries from Kyle Eastmond and Tom Biggs as well as 16 points from the boot of Tom Heathcote.
But, despite continuing what seems to be their ruthless charge up the Aviva Premiership table, Bath head coach Gary Gold is refusing to get carried away.
He said: "I don't think we're back in the title race after just one performance but I do think we've now given ourselves a chance. I think we'll keep our feet on the ground - we're not back in the title race just yet.
"Slowly but surely I think we're getting to where we want to be. I think we're making better decisions now about whether to kick or run but I also still think we're making awful decisions."