Mr Jones has been outspoken in his opposition to the Greens, in particular the party's stance on mining and fisheries, and has singled out Dr Norman and energy spokesman Gareth Hughes for criticism.
Ms Turei said: "I don't think that Shane has a grip on his emotions and I think that he lets fly regardless of whether it's sensible or not.''
She said his behaviour may have reflected his frustration with his role within Labour.
"When you're feeling frustrated and angry about your position, you don't necessarily always behave as rationally as you ought to.
"And maybe that's what's been driving his particular personal attacks on the Greens because they did seem to come out of the blue and [were] quite odd.''
She did not believe that his departure would improve Labour-Greens relations because Mr Jones was never part of the senior Labour team which negotiated with the Greens.
Ms Turei said his potential appointment as a Pacific economic ambassador was "odd'' and appeared to have happened quickly.
But she believed he was well-qualified for the role and said Pacific Islands did require assistance in negotiating with multinational fishing companies.
"He does have some expertise in this area. If he can do a good job in the Pacific, then all power to him.''
