The SNP minister said the Scottish Government indicated it would use its network of overseas offices in the EU to promote the country's interests "directly" with members states despite Brexit.
Among the areas of mutual interest where collaboration with European countries will be sought are climate change, Just Transition, green jobs, investment, education and the wellbeing economy, Mr Russell told MSPs at Holyrood.
"It's more important than ever that we continue to engage with the EU institutions and member states and we're determined we will continue our close ties with our EU neighbours with whom we have such close social, political and economic relationships," he said.
"The commitment is being delivered in a range of ways, including using the network of offices in Europe, Berlin, Brussels, Dublin and Paris who work to promote Scottish interests."
Mr Russell said this would also cover areas like democracy, equality and the rule of law "as we pave the way for Scotland's return to the EU as an equal, independent member state”.
The Cabinet Secretary said the need for direct relations had become even more acute after problems which have arisen over the last-ditch Brexit trade deal and holds-ups for goods at the EU border as a result of increased checks and bureaucracy.
"There are, of course, a plethora of arrangements put in place by the UK to continue dialogue with the EU, but unfortunately we have not had our notification of our involvement in any of them," Mr Russell said.
No meetings have taken place with UK ministers to discuss the outstanding "issues" arising as a result of the Brexit process, he added.
"I think it's very important now that we press our case on those issues and, of course, have our own direct conversations," he said.
"Scotland is not mute. Scotland is well recognised within the EU and therefore we need to make sure that we have dialogue directly and also, of course, make sure that we attempt to include what is taking place elsewhere."