The Scots remain in the mix to reach the 2018 World Cup finals in Russia following their 3-0 win in Lithuania on Friday.
First-half goals from Stuart Armstrong and Andy Robertson, and one after the break from James McArthur sealed the victory.
Strachan’s men are four points behind second-placed Slovakia, who face England at Wembley tomorrow while Scotland take on Malta at Hampden.
A win over Malta, who have yet to secure a point, and a victory for table-toppers England will keep Scotland’s hopes of securing a play-off place in their own hands going into the final two qualifiers against Slovakia and Slovenia.
The Scots face Slovakia at Hampden on Thursday, October 5, with the final qualifier in Slovenia on Sunday, October 8.
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Asked if he’d like to see England get the win, Strachan said: “Yes. They need to do themselves a favour because if they don’t do well and get beat Slovakia go top.
“When you’re England you have no option but to win games.”
Scotland have jumped up to third place in Group F and have taken seven points from their last three qualifiers to remain in the hunt for Russia.
But they will need to win their final three games to secure second spot, providing Slovakia drop points against England.
While Strachan is adamant the players never lost belief they could qualify, he feels the supporters are now beginning to do so as well.
“I think we are all feeling a bit better,” he said.
“We weren’t downhearted or depressed before.
“If they didn’t have belief they wouldn’t have done what they have over the last three games.”
Sheffield Wednesday midfielder Barry Bannan has withdrawn from the squad due to an ongoing injury.