Olsen called England's youthful team 'promising' after seeing his side beaten 1-0 in a friendly at Wembley, but he was unable to offer many positives for Hodgson ahead of the tournament in Brazil this summer.
After Daniel Sturridge's late goal saw England over the line, Olsen said: "Good luck in the World Cup - you will need it.
"I think that England have a young team with a lot of quickness - it's promising for the future but is it enough for the World Cup?
"I think we would have won if Christian Eriksen was playing."
But Hodgson leapt to the defence of his team, which included a number of players with limited international experience and had Southampton left-back Luke Shaw making his debut.
When told of Olsen's comments, he said: "I don't care about that. Every team will need good luck. We didn't need it tonight, that's for sure.
"This was an important game. It was important we put in a good performance. I wanted a level of energy, players running back when they lost the ball, making tackles from the wrong side, not being afraid to make mistakes knowing, with their pace, they can recover.
"That's what I did see and we put the icing on the cake with the goal to win it."