"I am delighted with the result and the fact that we are through to the final," said Barnett.
"We have improved in each game and now we have got to make another step up to face Spain. I am expecting them to be a much tougher side than when we played them last.
"They have been preparing for this tournament for quite some time and this is certainly their big tournament of the year.
"They'll be a completely different proposition and will be much stronger with home support."
England's victory came courtesy of two tries apiece for and Richmond wing Fran Matthews and Worcester centre Ceri Large.
Matthews' second-minute try put England on their way, and additional tries from Large and Old Albanians fly-half Sarah McKenna meant they led 19-0 at half-time.
First Matthews than Large grabbed their second tries after the break, before Bristol team-mates Nicola Hoole and Charlotte Male completed the rout.
Barnett said: "Russia were hard to break down and again this wasn't an easy game, but to now have three games where we haven't conceded any points is particularly pleasing.
"It has been a tough schedule and we have had three hard games, none of them have been easy wins.
"The younger players in the squad have also learned a lot and that is very important as part of this development process."