Striker Varney was on target as Pompey shrugged off Cotterill's departure to Nottingham Forest by beating Barnsley 2-0 at Fratton Park on Saturday.
Next up is a trip to Ipswich on Tuesday evening under caretaker bosses Stuart Gray and Guy Whittingham, and Varney is confident they can pick up another positive result.
He said: "We've got an experienced dressing room and I'm sure we've all lost managers in the past. You just have to stay professional.
"Obviously we're disappointed because we enjoyed working under Steve. We'll miss him and wish him all the best. But we've got a job to do for the fans, the new manager and the owners, so we're going to work our socks off to get some more wins.
"We've got a game on Tuesday night at Ipswich that we're all looking forward to and hopefully we can get back-to-back victories for the first time."