Fabio Capello's men have claimed maximum points from their first four qualifying games - without conceding a goal - but Northern Ireland still enjoy an outside chance of finishing in the top two after claiming three points from draws against Luxembourg, Portugal and Azerbaijan.
Russia meet Michael O'Neill's team in Belfast on Friday night and Anyukov urged his team-mates to stay 100 per cent focused at Windsor Park.
He told the Russian Football Union's official website: "It will be a difficult game and we need to concentrate, but we all know what our own strengths are.
"As long as we don't relax then all will be well. They are a good team who play an English style of football. In principle all the British teams are in the same vein."
Referring to Northern Ireland's result in Portugal, in which Helder Postiga denied the visitors all three points with a late goal, Anyukov added: "I wasn't surprised.
"Any team can take points from the group leaders, even outsiders for qualification. I repeat, the main thing for us is that we don't relax."
Capello should keep faith with goalkeeper Igor Akinfeev, who is looking to keep a 10th consecutive international clean sheet, while partnering Dynamo Moscow's Alexander Kokorin with Alexander Kerzhakov of Zenit St Petersburg in attack.
Northern Ireland boss O'Neill is looking for a first win since taking the job and can call on returning striker Martin Paterson while defender Chris Baird misses out through suspension.
Portugal, meanwhile, visit Ramat Gan with a view to wresting second place from Israel's grasp.
Eli Guttman's side currently edge the Selecao into third by virtue of a superior goal difference, generated principally through 6-0 and 3-0 victories over Luxembourg, who Portugal could only beat 2-1 in September.
Visiting coach Paulo Bento faces a nervous wait on the condition of Porto playmaker Joao Moutinho, who is struggling for fitness.
"I say this in all sincerity and using my common sense but Moutinho will not play unless he is 100 per cent ready," Bento said.
Luxembourg are ranked 151st in the world and host Azerbaijan, who have already earned creditable 1-1 draws against Israel and Northern Ireland. Luxembourg also took a point from the British team.