Partick Thistle might appeal against the red card shown to goalkeeper Scott Fox during the
Fox was dismissed by referee Craig Charleston after a tussle with Paul McGowan following the award of a Dundee penalty, which Gary Harkins missed.
Jags manager Alan Archibald told BBC Scotland: "By all accounts, the referee says it's violent conduct.
"Our goalkeeper says he just put his hand up to push someone away. If it's worthy of an appeal, we will."
But the Thistle manager was keen to acknowledge the contribution of Fox's replacement - Paul Gallacher.
"He did fantastically well," said Archibald.
"He had two great saves - obviously the penalty first and foremost - but he also got down for a header.
"That was half an hour we played with 10 men so we showed a bit of grit and determination.
"It's a good start but we know it could have been better if we'd taken our early chances.
"I thought we were very good in the first-half. We pressed the ball and moved it really well. We created a number of chances and never took them, apart from one wonder goal."
That strike was courtesy of Gary Fraser, who netted for the second time in two matches before Craig Wighton equalised for Dundee after the break.
"He's been brilliant for us and we're reaping the rewards of him having a good pre-season," added Archibald.
"He's got that in his locker and we're encouraging it all the time."