Managers Paul Hartley and Martin Canning were keen for more but agreed that a point apiece in was fair.
Canning, whose Accies side played most of the second half with 10 men following Dougie Imrie's dismissal, headed his team in front with five minutes to go.
But Greg Stewart scored his 14th goal of the season for Dundee to level the Scottish Premiership match at Dens Park.
Hartley told BBC Scotland: "Sometimes it's difficult to play against 10 men and I think we found that out today, but we'll take a point after going a goal down.
"I felt it was a missed opportunity today in terms of trying to get into the top six."
The point extended the Dark Blues' unbeaten run to six but a win would have lifted them above St Johnstone and into the top half of the table.
"We've kept the run going. They never give up," added the Dundee boss.
"We changed things in the second half but it just wasn't good enough in the final third.
"We've got to play better next week in the Scottish Cup game (against Celtic). A wee bit of the pressure will be off us. We'll be the underdogs. We're looking forward to it."
Hartley revealed that he hopes to sign a player before Monday's transfer deadline, but any addition will have to go some to match the contribution of Stewart.
"It was a terrific goal from Stewart again," said the manager.
"He came off the right-hand side today, but he has played in every position so far (in midfield and attack)
"It shows you we have a very talented player on our hands. I think he will keep progressing as a player."
For Accies' player-manager Canning, there was relief at ending a losing streak of four matches but frustration at the loss of the goal as full-time loomed.
He said: "The boys put in such a good shift. When you score a goal late like that you are thinking this is your day. I'm disappointed to have lost the goal.
"Coming up here with the run we were on, we would have taken a point. With 10 men, you would definitely have taken a point.
"When we went down to 10 men we had to change our shape a little bit. We were still a threat and we still broke well. At 11 v 11 we had two or three good chances.
"The pleasing thing for me is that the link-up play is good and we got in to positions to score.
"We won't get too high when we win and we won't get too low when we lose. The last four games haven't been kind to us in terms of results but performances have been there. Again today the performance was great."
Canning admitted he is "looking at one or two things" in terms of January transfers, and added: "At the moment the squad is good. They gel really well. They're a good bunch and they are all prepared to work for each other.
"They are young and enthusiastic and that's the most important thing.
"If we can get one or two in, we'll get them; if not, I'm comfortable with the group I've got."