Back, 31, takes over the captaincy of Leicester from Johnson following the England skipper's ban for foul play in the last round of the Cup against Saracens.
Brooke, the former All Black great, quit last Monday following a poor run in the Zurich Premiership. Wilson says: "There was no inkling that Zinny intended to resign.
"When it was announced the players were surprised and how we cope with it depends on how guys knuckle down and get on with it.
"I still have high expectations of the club doing very well. But it is about staying positive and my job off the field is to to keep morale high.
"We are at the start of a new year and there is still a lot of rugby left. Let's hope the semi-final will be a good stepping stone.
"Leicester is a very tough assignment. It's a challenge which the blokes will look to grasp.
"We are not expected to win but we only narrowly lost the last time they played here."
Quins used to step up a gear for the Cup but it is eight years since they ended their run of three finals in a row.
Leicester, chasing glory at home and in Europe, look too hard-nosed to let this one slip and should be playing Newcastle, who are at home to Sale, in the final at Twickenham on 24 February.
