Cohen was speaking at the Knockout quarter-final draw on Monday, where Swallows were pitted against SuperSport United.
“The [determination] is very high and everybody wants to win a trophy this season in the squad, so the determination for us to win the trophy is there,” Cohen said.
“If we look at it, it’s only another three or four games and we’re there.
“So if just go out there and work hard, anything can happen.”
The two teams have already met this season, with Swallows claiming a comfortable 2-1 victory in a Premiership encounter last month.
Cohen said the team was looking to build on that result and continue to fight in their search for silverware.
“We take each game as it comes and it’ll be a different game to the last game, but if we go out there and play the way we’re used to playing, the result will go our way,” Cohen said.
“We have to continue, it’s still early in the season and we just have to keep going.
“Our goal is to finish as high as possible. A top four, top-five finish will be good for us and hopefully we win a trophy on the way.”
Meanwhile, Platinum Stars will look to build on their early success this season, after they were drawn to face Mamelodi Sundowns in the quarter-finals.
Stars lifted the MTN8 trophy last weekend by beating Orlando Pirates and could slay another giant when they take on the Brazilians at home.
“We’ve got a very good track record against Sundowns and we want to continue with that,” Stars’ striker Patrick Malokase said of the draw.
“The fact that we’re playing at home is a very good advantage for us. We’ll prepare very well against a good side and hopefully do our best.”
The prospect of taking on Stars in their own backyard will be a daunting one for Sundowns, whose coach Pitso Mosimane has described Dikwena as their ‘hoodoo’ side, following a 1-1 league stalemate in August.
On Sunday, Stars and Maritzburg United were forced to take two water-breaks in either half as the temperature in Moruleng, near Rustenburg, reached 35 degrees.
Malokase said the team had grown used to the searing heat of the North West province and would look to use their experience to their advantage when Sundowns visit.
“The North West province is very hot outside. I think it’s very difficult mostly for teams coming to play there,” he said.
“But we’re training well. We don’t rely on the weather, we’re doing our part on the field of play.
“We’re running, we’re playing a good brand of football and we’re winning games, which is the most important thing for the team.
“If we play at night, we try by all means to make our training sessions at night, same goes for the day.”
The first round of fixtures were yet to be concluded when the draw for the quarter-finals took place, with Orlando Pirates and Mpumalanga Black Aces wrapping-up the round at Mbombela Stadium in Nelspruit on Tuesday.
The fixture was originally scheduled for last week, but due to the Buccaneers’ Caf Champions League commitments, the match was delayed for a week.
Orlando Pirates will take on Golden Arrows should they progress, while Black Aces face a potential meeting with defending league champions Kaizer Chiefs, should they beat Pirates.
If Aces go through, Free State Stars will play Golden Arrows, but if Pirates progress, Stars will then play the Amakhosi.
Telkom Knockout quarter-final draw: Orlando Pirates/Free State Stars v Golden Arrows, Platinum Stars v Mamelodi Sundowns, Mpumalanga Black Aces/Free State Stars v Kaizer Chiefs, SuperSport United v Moroka Swallows.