The row from the Boxing Day clash involving the Paisley skipper and United youngster Stuart Armstrong refuses to die down.
Goodwin is expected to find out on Monday if he will be punished by the Scottish Football Association for ramming his arm into Armstrong's face as he slid in to tackle the Scotland Under-21 cap during Saints' 4-1 win last week.
But Lennon is angry that Tannadice bosses posted stand-alone footage of the incident on their YouTube page, with links also posted on their Twitter and Facebook accounts, in an apparent bid to draw the attention of SFA compliance officer Vincent Lunny.
Reports have suggested the Arabs could also be in trouble for "not acting in the best interests of the game", while Lennon insists it is a ploy St Mirren would never consider.
Asked about his thoughts on the YouTube row, the Buddies boss told Press Association Sport: "My football club would not do that. It's not in the make-up of our club to be putting anything out there [on social media].
"With the very good coverage that the BBC give our game, nothing would go unseen by the SFA and the disciplinary panel.
"So I found it a little bit strange that another club would do that. We all work in different ways but that was a first for me."
Lennon had to substitute his skipper before he was sent off against United but Goodwin was back in the Saints side that drew 1-1 with Hearts at home on Sunday.
However, the Saints manager is unsure if he will be able to call on the player for Thursday's trip to Kilmarnock and is waiting to hear what action Lunny will take.
But he insists the Irishman still has his backing, saying: "Jim has fantastic qualities but like anyone he has weaknesses. However, what he brings to this football club as captain and by being a terrific guy off the pitch and a winner on it is great, so I'd rather focus on his qualities."