Aberdeen cut the gap on Scottish Premiership leaders Celtic to three points with a 3-0 victory over Hamilton on Sunday, which would have been even more convincing but for a series of blunders from referee Willie Collum and his team.
Celtic and Aberdeen meet at Parkhead on March 1 and much is expected of the contest given Aberdeen have taken 32 points from a possible 36 since last losing in the league against Celtic, a game which they should have taken more from.
But Considine is maintaining full focus on facing a St Mirren side battling for survival near the bottom of the table.
The defender told RedTV: "It's going to be a huge end to the season but we have got St Mirren next and we will look at that and take each game as it comes."
Aberdeen will draw level with Celtic if they beat St Mirren as Ronny Deila's side do not play Hamilton until Sunday.
But Considine doubts whether Celtic will feel much pressure given they also face two Europa League games against Inter Milan before hosting the Dons.
The 27-year-old said: "Celtic are used to pressure, let's be honest, they have a big game on Thursday night. Our heads are on next weekend.
"When the Celtic game comes around we'll sort ourselves out for that."
Considine had a major impact on Sunday's game at New Douglas Park. The left-back slammed home the opener from close range, saw a headed goal disallowed for a foul, saw David Goodwillie wrongly punished for offside after turning home his flick-on, and came close to scoring on several other occasions - watch the highlights here.
"It was just one of those games, that a lot of the crosses come to you and fall on your head," he said.
"But it was great to get a goal. That's two for the season now and I'm more than happy to be chipping in."
Source: PA