The Dons were trailing 1-0 to ten-man Rangers in the Ladbrokes Premiership opener at Pittodrie last Sunday but kept plugging away until youngster Bruce Anderson scored an added-time leveller.
It was another positive sign for Considine who told the club’s official website: “The game on Sunday shows that hunger, desire and fitness that we have [to score late on] and we are a team that we keep going right until the end.
“I always find when you play against the likes of Celtic you can hold them off for 90-odd minutes and then the last kick of the ball they can go up the park and score.
“I think that’s something you could really do with having in a team and I feel that since the manager has come in, we feel if we don’t score early there’s less pressure.
“It’s great young Brucey scoring as well. I am so pleased for him. He deserved the chance and he definitely took it when he came on.”
A tough Europa League tie last Thursday night against Burnley came before the visit of the Ibrox side and Considine enjoyed a week to prepare for the trip to Tayside.
He said: “It’s going to be a very tough game this Saturday. It always is at Dens Park and it will be a tight game. We’ve got a good record down there, but every season is different. They’ve recruited well and it will be a very tough game.
“We’ve had a really good week training-wise. We managed to relax a bit on Monday and Tuesday and then got back into training. The manager has got us back up to speed and everyone’s looking sharp and other than the injuries we’ve got everyone’s looking good.”
Dundee manager Neil McCann insists there is “nothing happening” in relation to a deal bringing Lawrence Shankland to Dens Park.
The Ayr striker, who has started the season in scintillating form with nine goals in five games, has been linked with a move to Dundee in recent weeks. It was reported on Thursday that the newly- promoted Championship club had rejected a bid from an English side for their striker, but McCann, who has made it clear he is keen to add to his attacking options, played down his interest.
“It’s really unfair to comment on any players I am after,” he said. “What I would say is that I have been in the market and been actively trying to get players. Some have come close and fallen through, others not.
“Lawrence is a very talented player. I know him from my time at Dunfermline and have no doubt he could come to a club like Dundee and do very well, especially in the Premiership. But as it stands there is nothing happening.”
He added: “We tried to do some business on Thursday, it didn’t quite happen but we will continue working on that.”
Despite not managing to strengthen, McCann was left relieved after managing to hold on to a couple of key players as the English transfer window shut on Thursday afternoon. Glen Kamara and Steven Caulker were both linked with a move down south – with Leeds rumoured to be interested in the latter – but they remain with Dundee.
“There have been no official bids put on the table yet for Steven,” said McCann. “Clearly he is a player that attracts a lot of interest. The good thing is, I thought he would probably go and we would lose him, but we still have him.”