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But the Well boss will not walk away from the relegation battle.
"I'd be arrogant if I thought a 7-2 defeat at Aberdeen and a 5-1 loss at home doesn't put me under pressure - of course it does," McGhee told BBC Scotland.
"But I believe we've got a decent group of players here."
Motherwell were without experienced defenders Stephen McManus, Stevie Hammell and Richard Tait through injury and their replacements failed to handle the threat of the Dundee attack.
In fact, Fir Park centre back Zak Jules started the scoring for Dundee with an early own goal.
"We've been slightly undermined by the loss of experienced defenders and we've suffered from that today," added McGhee, who was the target of a fans' protest outside Fir Park after the match.
"The first half defensively was poor and they didn't cope with anything that was thrown into the box. We were too easy to score against and we actually didn't look like a back four until we changed it around and Carl McHugh went into centre half later in the game.
"But otherwise I will take the team out there in the week and look at the video of what happened and we'll try and help Joe Chalmers and Zak Jules and Jack McMillan to improve on what happened today.
"They're three young players with very little experience between them but we've got to make sure in experiencing defeat like that they improve. That's all I can do.
"Until somebody tells me something different I'll be here on Monday to do that with Steve Robinson and James McFadden."
Despite having won only two of their last 13 Premiership matches, McGhee still feels his squad has the capabilities to escape relegation.
He said: "Of course we do, there are six other teams in the heat of the relegation battle so we know at some point we're going to have to win games.
"But all we can do is on the training ground, pick the strongest team we have available and go to Kilmarnock next week and try and win."
Mark McGhee admits he is under pressure after Motherwell's 5-1 home thrashing by Dundee left them three points off bottom spot in the Premiership.