They doubled that lead but Liverpool grabbed a goal back and in the end it was backs-to-the-wall stuff at Anfield.
"I felt we deserved it in the end, even if they did throw everything at us towards the end. It was a case of 'Fasten your seat belts and hang on' and we managed that," Strachan said after the game at Anfield.
"We defended well as a unit, and as individuals. We were brave at the back and quick and pacy up front.
"We handled the fact that we lost Claus Lundekvam with an ankle injury and had to reshuffle our defence. But we stuck together and got what we deserved.
"Our front two, Ormerod and Beattie, caused them a lot of trouble with their pace.
"We could have had a couple more before they scored, and then we had to hang on. I have every sympathy for Gerard, and anyone who wants to be a Premiership manager. It can be tough.
"If I was a multi-millionaire I would buy a golf course and knock balls around all day, and certainly not be doing this."