The Hoops went top with the victory, but it came at a price as Dutchman Vennegor joined their crocked list.
Defender Mark Wilson will jet out to America for a consultation with knee specialist Dr Richard Steadman next week, while talismanic midfielder Shunsuke Nakamura has missed the last three matches with a knee injury and is doubtful for the Champions League clash with AC Milan on Wednesday.
Strachan tried to be pragmatic about his latest injury blow, saying: "Jan suffered a hamstring injury after taking a shot and it doesn't look good.
"I think it is an outside chance for him.
"We will just get on with it. We have lost a lot of players over the last few weeks and we just get over it.
"Nakamura had a sandwich in his mouth and his interpreter wasn't there so I was struggling (to speak to him).
"But he will be in on Sunday and we will definitely make up our mind on Monday."