Russia's 267-strong team has been banned from next month's Paralympic Games in Rio because of state-sponsored doping uncovered in the McLaren Report.
"We feel great sympathy for those athletes," Spence told the BBC.
"But I think the apology needs to come from those who are leading this state-sponsored doping programme in Russia."
Russian athletes were permitted to compete at the Rio Olympic Games if their sport's governing body allowed them, but the International Paralympic Committee has taken a tougher stance.
The Court of Arbitration for Sport (Cas) announced on Tuesday that they had upheld the International Paralympic Committee's (IPC) ban on all Russian competitors.
Russia's Prime Minister Dmitry Medvedev said: "The investigation about the Russian doping is a thick and disgusting mix containing 80% of politics and 20% of the actual doping, the politics targeting against sports, Russian athletes and Russia as a country."
Russian TV on Tuesday carried interviews with Paralympic athletes denied the chance to compete in Rio, among them track-and-field athlete Alexei Ashapatov.
"When they tell us that we do not meet Paralympic standards, I don't know what to do," he said. "You do all you can to develop Paralympic sports and then you are accused of not meeting those standards.
"I don't understand the officials who made such a harsh decision."
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Andrei Strokin, five-time Paralympic swimming champion, said the decision was "cynical" and "baseless".
However, Spence - the IPC's director of media and communications - insisted it was those behind the Russian doping system who should shoulder the blame.
"It's because of them - the people at the very top - who have introduced this system where there's doping across all sports as shown in the McLaren Report," said Spence.
"It is they who are responsible for this and that is why we have had to take this decision.
"It needs to change or the Russian Paralympic Committee will continue to be suspended, or won't be able to compete in further Paralympic Games or IPC sanctioned world championships."
A further appeal by Russia to Switzerland's federal court is possible, but it is unlikely to take place before the Games open in Rio on 7 September.
"Long-term we hope this is a catalyst for Russia and that the state-sponsored doping system which is plaguing their sport at the moment disappears," Spence told BBC Radio 5 live.
"We really want the Russian team back competing, but we only want that to happen if we can ensure a level playing field for all our athletes."
Officials behind Russia's state-sponsored doping should apologise to its athletes, International Paralympic Committee spokesman Craig Spence says.