Gloucester’s chief executive Alex Brown said earlier this month that the club “have to get this European final right”.
A review of the season will be conducted over the summer although Brown said Skivington – who is under contract – had the club’s backing.
Gloucester are unbeaten in the Challenge Cup, having been the only team in the competition to come through the group stage without a loss.
They beat Castres, Ospreys and Benetton in the knockout stages to reach their fifth Challenge Cup final, a competition Gloucester won in 2006 and 2015.
“The emotion is pretty solid, this week will be heightened,” Skivington said.
“We don’t need to talk too much about it – it’s a final and obviously we’ll review who we’re up against but I think everyone is well aware of that.
“You play because you want to get to finals at the end of the season and the lads have earnt the right to go to Tottenham and have a crack.”
Skivington said the prospect of a record-equalling third Challenge Cup title to take them level with Clermont and Harlequins would be “great for the club”.
“We try to get some silverware in the club, there’s not a lot of trophies in the cabinet,” he said.
“We shifted tact slightly when we knew one of them [Premiership] was out of reach but for me it’s really important – the more finals we get to hopefully will lead to more trophies.”