Paul Hartley’s side make the trip to the Capital hoping to cause an upset against Scottish Premiership opposition and Stevenson is wary of the League One leaders’ threat.
“They are flying just now. We played them last season and we were lucky to win. They were the better team in my opinion. It was a good win in the end for us but I think they’ve improved since then. It is going to be a tough game and is not one we are underestimating," the left-back said as he previewed the fourth-round clash.
“They don’t just have good individual players, tactically I thought they were very good. They caused us lots of problems. We have done a lot of work on them and know how they are going to approach this one.
“But we have probably improved since then as well. We probably play a different style now to what we did before.”
Stevenson started and played the bulk of Hibs' Premier Sports Cup final defeat by Celtic last month and admits the chance to progress in the other domestic cup competition is one the Capital club must take.
“We have had great runs in the cups recently, but it’s almost like you build yourself up for a greater fall. It’s that next step that we need to take, picking up the silverware. We have been runners-up on many occasions. It has been disappointing – you’re only remembered when you win the cup,” Stevenson states.
"But we need to focus on Cove at the moment.”
Hibs are no strangers to the last four of cup competitions, having made the semis seven times in the last ten years, and Stevenson is eager to make it count this year.
“It is good to go on a run in the competition – it can give the fans and good day out and bring in money to the club. I am sure teams see us as a big dog and know we are wanting to go on a good cup run, but we take nothing for granted.
“Four semi-finals ago I thought it might be my last time at Hampden, so I have managed to get there quite a lot since. But you never know when it’s going to be your last chance so I have to make the most of it.”
Stevenson is relishing working under Shaun Maloney – his twelfth manager at Easter Road – and feels he has learned a lot since the 38-year-old’s arrival.
“In three or four weeks I have learned so much. We are playing a different formation to any I have played in my years in the game. There are little technical things, little defensive things, which are different. It keeps things fresh, it keeps me focused,” he explained.
“I don’t know if I can say what he wants the full-backs to do because I will give our tactics away, but there are little things which are totally different to what I was used to.”