The Scots' failure to beat Argentina last weekend means they will be eliminated from the competition at the pool stage for the first time in their history if they fail to beat England by eight points or more in Auckland on Saturday.
Despite the bookmakers making England overwhelming favourites to beat Scotland and advance to the last eight, head coach Robinson is convinced he can beat the country he used to coach for two years.
Since he took on his role at Murrayfield, Robinson has led Scotland to victories over Australia and South Africa and also made history by becoming the first Scotland coach to win a series in the southern hemisphere last year when his side beat Argentina in a two-Test series.
Robinson's position will undoubtedly come under question if Scotland bow out so early in the competition, but Logan is adamant that the 47-year-old is doing the best he can with such limited resources available to him.
Logan, who represented Scotland 70 times, said: "Since Andy Robinson came in there has been a lot of great performances and not as many average ones as we used to have.
"He has not got loads of players available to him. There are poor resources.
"Hopefully if we don't qualify, he will stay on as coach because he's a great coach.
"We need to concentrate on addressing the other problems we have in Scottish rugby instead.
"We need to be getting more people playing more rugby in Scotland, we need to get more professional teams and give kids more opportunities so they can play for their country. We have only two professional teams and quite frankly it's not enough."
Given their series victory in Argentina, many thought Scotland would have beaten the Pumas last weekend and it looked as if it was going that way until they threw away a six point lead with eight minutes remaining to lose 13-12.
That leaves them needing to beat England by eight points or more to secure qualification from Pool B if, as expected, Argentina comprehensively beat Georgia.
Logan thinks England are nowhere near as good as they were when they last won the Webb Ellis trophy in 2003, or in 2007 when they reached the final, but still does not expect Scotland to qualify.
"England are ranked fourth in the world. I think we can beat them but not beat them by eight points," said Logan, who was speaking at Twickenham to publicise December's Heroes Rugby Match.
"England will just be thinking 'let's just win this game and then we are through'."
England have scored 17 tries to Scotland's four during the tournament in New Zealand, with their most recent victory coming last weekend in a 67-3 hammering of Romania.
They have not quite been at their best yet, however, and the huge victory margin over Romania came as the Oaks were resting a number of their players for the game against Georgia - a match crucial to their hopes of qualifying for the next World Cup in 2015.
England's preparations have also been hit by lurid headlines about a team night out after the win over Argentina.
Logan thinks the red rose could make the final given the teams they are likely to face in the quarter-finals - France and Ireland or Wales - but still thinks they are not a cohesive enough unit to merit winning the competition.
"England have good players but they just don't look like a team for me," the former Wasps wing said.
"They look like two units - a set of forwards and a set of backs. "They don't seem like they did in 2003. There was a blend back then and I don't see that now.
"Their centres look pretty straightforward and the team is not as good if Moody is not in it.
"If I were Scotland I would put pressure on England's front five. I'd put pressure on Courtney Lawes and Louis Deacon in particular. "I don't think Deacon should be in the team. You never see him with the ball in his hands.
"I think Scotland's front row is better than England's too."
:: Kenny Logan will take part in the Heroes Rugby Challenge, which will be played at Twickenham Stadium on Saturday 3 December 2011. The game aims to raise a substantial sum of money for Help for Heroes, the charity which provides practical support for wounded service men and women.
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