The Scottish FA has unanimously backed Strachan to carry on as national coach despite back-to-back 3-0 defeats in away games against Slovakia and England.
McGhee, the Scotland No 2, believes Strachan can revive the campaign, citing the impressive start the side made against England at Wembley last Friday as evidence.
“It showed in the performance that he got his message across and the boys responded and played very, very well,” McGhee said. “He is entitled to go into the next games and see if we can improve on the results.”
Scotland were eventually well beaten at Wembley and have just four points from their first four qualifers and lie second bottom of Group F with six games to play.
They took seven points from their first four matches in their Euro 2016 campaign from arguably a tougher run of fixtures, against Germany, Georgia, Poland and the Republic of Ireland. But McGhee bristled at the suggestion that there were no signs of progress.
“In some ways our results and overall performance in the last campaign is better than it is in this campaign,” he said. “However you have to be honest, you have to look at the players we have available, look at the opposition.
“Don’t judge it as the same thing, things evolve. Circumstances in each game are different. You can’t be blind where you don’t take account of any other circumstance other than the result. That’s not fair. Last time we had a great result and performance against Ireland.
“We have not had one of those big results and performances yet. But that’s what we are working towards. We were close to it at Wembley in some ways and that’s what we will take into the next game, that we want that big performance.
“I feel if we go into that game and it was to be abject then there are clearly questions that need to be asked. But I feel so far that Gordon has done just about as well as we could be expected to do.”
Scotland’s next two qualifers are at home, with the visit of Slovenia on 26 March and the return against England on 10 June.
Speaking before the SFA announcement on Strachan, McGhee, pictured, said: “As far as I am concerned, I am looking forward to the next games, in particular I cannot wait for the game in June. I want to get the other games, of course I do, and I want to do well but I want to be here when we play England at Hampden. Whatever else anyone says, we will just keep doing it until someone else takes the keys off us and we can’t do it.”
Four of Scotland’s six remaining qualifiers are at home but it will take a mighty effort to turn around a campaign which has Strachan’s side trailing group leaders England by six points already.
Only the group winners qualify automatically for Russia 2018, with the eight best runners-up from the nine European group going into play-offs.