The Scots moved into third place in Group F on Friday evening with a 3-0 win in Lithuania, ahead of their home game against Malta on Monday night.
Strachan's side are unbeaten in their last three qualifiers and now sit six points behind England and four behind Slovakia, who meet at Wembley in their next fixture.
Scotland still probably need three wins from their final three qualifiers to claim a playoff spot, but their position is healthier than when they lost 3-0 in England last November to leave them with four points from as many games.
Strachan told Sky Sports News: "The belief has always come from the group of players we have got, which has evolved over the last year for different reasons - confidence, injuries, people playing better, their club sides doing better.
"But I have never had any doubts in the players really, and because we have never had any doubts with each other we could come back from not being in a good place.
"If we didn't believe in ourselves, when you are not on a good place you can't get out of it. We have dragged ourselves out of the bad place and we could only have done that if we believed in each other and enjoy working with each other."
Scotland last reached a major tournament in 1998.