Kevin Thomson's first ever goal for Rangers just before half-time was enough to keep the three points at Ibrox.
And the Celtic manager admitted the league title is creeping out of sight.
"It is going to be very difficult, but we have two Old Firm games at home and if we play like we did in the first half then we have a chance," said Strachan.
"But if we defend like we did today and Rangers get another chance then it could be a problem."
The Celtic manager once again lamented his team passing up goal-scoring opportunities.
"We didn't take our chances and that came back to bite us," said Strachan.
"The more balanced people would say that we deserved to take something from the game and on a good day we would have got more.
"In the first half, we were composed, we were brave, and for a team that's chasing their rivals we put up a right good showing.
"But I've learned that the first goal in these games is important and the goal changed the game, that's for sure."
The Celtic manager added that his team's second-half display was one-dimensional, but still found cause for optimism.
"If you go through the team, Hinkel had a good game, Caldwell did well, apart from one pass.
"Boruc had a good save and the two front men Jan Vennegoor of Hesselink and Georgios Samaras gave them problems.
"I think that's the best our wider men, Aiden McGeady and Shunsuke Nakamura have been as a partnership in a game against Rangers.
"So we had a lot of very good things going for us."
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