Aberdeen trail sixth-placed Hearts by seven points, St Johnstone by four, and have five games remaining until the league splits.
But after declaring the Perth match 'win or bust' for their top-six hopes, McGhee admits the latter now rings true.
He said: "We now have to concentrate on just seeing when we can win our next game.
"I don't think we should fantasise that we are going to win all of our games convincingly enough to finish in the top six.
"That is a huge disappointment. I think losing Lee Miller (to Middlesbrough) at Christmas has turned out to be more difficult than we imagined maybe, but we had no choice in that.
"But I still think over the season we might have had enough to finish in the top six and we haven't."
McGhee, who has lost Gary McDonald to a hamstring injury for a number of weeks, admits his side - winless since late January at Hearts - must improve quickly or risk the end of their Pittodrie careers.
He added: "I don't think we played well and I think therefore the result was about right.
"But that's what has been happening in recent weeks. We didn't get better tonight and that was disappointing.
"We will continue to try and improve it through to the end of the season. "We know there are a lot of players coming out of contract, there will be a lot of change in the summer.
"I continue in the background to make preparations for that. But, in the meantime, we want to get better, want to win some games and we will continue to try and do that."
Meanwhile, St Johnstone manager Derek McInnes continues to enjoy a dream season on the club's return to the SPL after a seven-year absence.
The seventh-placed Perth outfit are now only three points behind Hearts and boast two games in hand on the Edinburgh outfit.
McInnes hailed his players for delivering another triumph, especially in the face of a growing injury crisis.
With Celtic to come at Parkhead on Saturday, he said: "It was a very good three points, a good night's work.
"I felt the players treated it the way it had to be. I thought we were relentless with our pressing and effort, trying to force errors with some good play as well.
"The enthusiasm and appetite from the team was different class and they deserve all the credit for that.
"But we're having a heck of a time with injuries. I think we had 10 injuries going into the game, four centre-halves out, four centre-forwards and two midfielders.
"Kevin Moon has now picked up a medial ligament strain and we don't have Cillian Sheridan for the Celtic game on Saturday, so we are effectively 12 players down for the weekend."
McInnes admits trying to overhaul Hearts is now his side's next target.
He added: "It's another important three points, another of our games in hand won.
"You are always looking over your shoulder. We tried to stress the point when we came up that we had to try and make sure we are an SPL club next season.
"The way results have been, obviously it's an important period over the next two to three weeks, you've got to try and motivate the players and set targets as you go along.
"We just look to try and go above the next team which is Hearts. If we show the same appetite, you never know."