The Three Lions looked to be heading for victory in Saturday’s clash in Marseille thanks to Eric Dier's thunderous free-kick but an injury-time equaliser from Vasili Berezutski forced them to settle for a point.
Roy Hodgson's men now face a crucial clash against Wales, who are top of the group after beating Slovakia, but Redknapp insists England will have “no problems” reaching the last 16.
“We'll come out of the group no problem. The Wales game is going to be a big, interesting game,” he told Betsafe.
“I think [Roy] Hodgson will be happy with the way we played – especially during the first half. Harry Kane was quiet, but I think Roy will play him at the start again. If he makes a change, I think he'll replace Sterling.
“[Jamie] Vardy is one that could come off the bench. We need to win. We don't want to be going into the last game against Slovakia needing to win to qualify. I think England will beat Wales.”
Despite his confidence, Redknapp does feel that England ought to have beaten Russia comfortably and was surprised not to see Jamie Vardy introduced as a substitute.
“[It was a] disappointing result in the end. The worst Russian team I've seen, they were so poor it was embarrassing,” he added.
“I don't know where they found some of those players - they wouldn't get in a Vauxhall Conference. The opposition was poor – we made them look poor.
“We could have been three or four up at half time. In the first half we played ever so well – I was very, very pleased with England first half, but we didn't stick our chances away."