The referendum, in which 97 per cent of voters reportedly voted to leave Ukraine, has received widespread criticism from the west, and, in responding to the escalating crisis, Europe's foreign affairs council has imposed targeted sanctions against 21 Russian officials.
Speaking following the council, Ashton said, "We had an in-depth discussion about the latest developments in Ukraine, including [Monday's] so-called referendum in Crimea.
"We recall that deployment of Russian forces is a violation of Russia's international commitments. Let me stress that the EU does not and cannot recognise the outcome of a referendum under these circumstances.
The British official continued, "We also deplore the further negative developments we have seen on the ground, which are in clear violation of Ukraine's sovereignty and territorial integrity. We do regret that Russia has so far not engaged in negotiations with Ukraine.
"In the absence of positive steps and in line with the statement of EU leaders on 6 March, we have today decided to introduce additional measures, more specifically restrictive measures against 21 individuals responsible for actions which undermine or threaten the territorial integrity, sovereignty and independence of Ukraine."
Although many welcomed the targeted visa bans and asset freezes, which come with a threat of further action if Russia fails to engage with the Ukraine, others feel that the European response lacks teeth given the brevity of the situation.
Elmar Brok, who heads up parliament's foreign affairs committee, responded positively to the news saying, "The targeted sanctions against Russia now on the table are just the beginning for as long as Russia does not change its strategy of gradual escalation.
But the EPP deputy remained optimistic that a positive outcome can be achieved, "I do believe... with good will from all sides, in the possibility to reinstate respect for international law in order to ensure freedom, sovereignty and territorial integrity and to include the security interests of Russia," he said.
"For this reason, Russia must be ready to quickly come to the negotiating table to contribute to an agreement without delay. A contact group of the [Organisation for security and co-operation in Europe (OSCE)] and of the Budapest memorandum involving the EU may be an example for this," the German MEP finished.
Greens/EFA co-president Rebecca Harms agreed that the sanctions are "the correct response", and emphasised that, "If Russia continues to disregard international diplomatic efforts, further sanctions must follow."
"The EU must now do everything possible to safeguard the rights of minorities in the Crimea. It must continue to insist that a strong OSCE observer mission travels immediately to the east of Ukraine and the Crimea. The preparation and conduct of the election in May must be without pressure."
But, other MEPs were more outspoken in their criticism of Russian president Vladimir Putin's behaviour, with Warner Schulz, Green MEP and vice-chair of parliament's EU-Russia committee, saying, "Putin's actions in Ukraine represent the return of aggressive nationalism, which aims to reunify Russians beyond Russia's borders.
"Turning a blind eye to 'keep the peace' will only confirm Putin in his aggression course. Only the resolute defence of international law can secure a peaceful future for us and our eastern neighbours.
"If Russia continues to deny any negotiations with the OSCE, EU heads of state and government have to impose economic sanctions on Thursday [at the European council meeting], even if it has an impact on the EU itself. There can be no appeasement because of economic interests."
Elsewhere, UK MEP Richard Howitt expressed reservation over the effectiveness of sanctions in the current situation, saying, "Western politicians keep threatening 'costs' on Russia, but it is difficult to believe Vladimir Putin will consider today's EU sanctions to be ones which are truly costly.
"Essentially these are political not economic sanctions, where the Russian oligarchs continue to get off scot-free.
"I fear protests such as the ones we've begun to see in Donetsk and Kharkiv are more likely to be used as an excuse for further military intervention by Moscow before the diplomatic breakthrough [Monday's] European decision hopes to achieve," he warned, adding, "It may be that we see provocation before de-escalation,".
And Hannes Swoboda, who leads parliament's S&D group, was also forthcoming with his opinion of Putin's role in the escalating crisis, saying, "[He] has revealed his true colours by ignoring the protests from the entire international community against the illegitimate and illegal Crimea referendum.
"All legitimate referendums, from East Timor to South Sudan, have required years of preparation, consultation and observation to gain legitimacy and international acceptance. The referendum and Crimea's request to be annexed by Russia, are invalid in the eyes of the world," he explained.
"In reality, Putin is now more isolated than ever: none of the potential candidates for his Eurasian Union can accept his aggressive behaviour any longer, for fear of his intentions towards their own citizens and land. Putin has gained nothing in Ukraine, but he has lost his Eurasian Union dream.
"We call for a swift, large-scale OSCE mission to be deployed in eastern and southern Ukraine, to record all irregularities and contain the crisis.
"The Ukrainian government must lead by example and proceed with fundamental reforms, including fighting corruption and protecting the rights of all minorities. These are some of the key political conditions for signing the first part of the association agreement with the EU. Following the presidential elections in May, parliamentary elections must be scheduled to form a fully inclusive government of national unity, representing all factions and groups," he concluded.
Putin has since signed a decree recognising Crimea as a sovereign state.