Saints won 13 trophies under Harrison, who has left after five and a half years in charge to join Hartlepool.
Ruscoe, 39, is in interim charge along with Steve Evans following Harrison's departure.
"He's won so many [trophies] and he's done such a good job, how do you go and follow that now?" Ruscoe said.
"Me and Steve want to give it our best and the lads will as well. They've been great in the last few days as we've taken over."
Saints begin their preparations for the Champions League qualifiers with a friendly against an Anglesey Island Games XI on Tuesday, 6 June.
Club owner Mike Harris hopes Ruscoe and Evans will be permanent replacements, but says one of them must complete their coaching qualifications.
Former club captain Ruscoe, who joined Saints as a player in 2001 and holds a Uefa A coaching licence, wants the job on a permanent basis.
"I've been in football full-time for over 20 years so it's something I want to do for the rest of my career," Ruscoe told BBC Radio Shropshire.
Interim manager Scott Ruscoe says Craig Harrison will be a hard act to follow at Welsh Premier League champions New Saints.