The SFA board this month backed Strachan following their review of a 3-0 defeat by England that leaves the Scots fifth in their qualifying group.
"We expected more," McRae said of Scotland's points total.
"But we still have the confidence in Gordon to try to get to that play-off slot. That's the one we had aimed on."
Scotland trail Group F leaders England by six points and second top Slovenia, who are their next opponents, by four.
"We have a bit more to do now, but four games at home and everything to play for," McRae told BBC Scotland.
"March will be the next home game, a great opportunity to get a win.
"Gordon is a good experienced coach, a former international player, he has all the credentials, he has won trophies.
"He has a good group of players, they work as a group.
"We are obviously a bit disappointed to say the least in terms of four points from 12 which, if it had been six or seven we would have all have had at least a half smile on our face.
"But it is mathematically possible and I still think Gordon can take us to the play-offs."
McRae confirmed the quest to find a new performance director to replace Brian McClair, who left in July, is ongoing.
However, he would not comment specifically on former Cardiff City, Watford and Wigan Athletic manager Malky Mackay, who is believed to be one of the candidates and who was at Hampden Park with McRae on Sunday for Celtic's 3-0 Scottish League Cup win over Aberdeen.
"The update is quite simple, the process is well on, a series of interviews have been taken and it is ongoing," he said.
"I am not going to comment on any individual who might or might not be part of that process.
"It is very important. As you know, the performance strategy started about five years ago and there is a good lot of work going on just now and we are looking forward to changing things, tweaking things, to say the least and get the new performance director in and try to move on from there."
Scottish FA president Alan McRae remains confident that Gordon Strachan can take the national side to the 2018 World Cup finals.