Following successive defeats to QPR, Rotherham in the Capital One Cup, and Burnley the Owls got up and running for the new campaign at Elland Road.
Owls winger Michail Antonio forced Leeds goalkeeper Paddy Kenny into two crucial saves in the closing stages when both sides chased the winner.
"We played well and I think most managers would have taken a point from Elland Road before the game," said Jones.
"But I thought we should have taken all three points. We had the chances, we might have had a penalty and in the end we were unlucky.
"We should have done better for their goal and we will continue to work on those situations. But overall we have done ok, we are off the mark and now we move on to the next game."
"He came into the team today on the back of three days training and you wouldn't have thought he had been away."