The West Ham United boss is delighted with the full-back's progress but says he still has a long way to go.
And Allardyce admits his scouts and staff all urged him to sign Cresswell after seeing him in action, although the defender still has 'some way to go.'
"I’m sure Aaron Cresswell, a Liverpool fan as a youngster, will be keen to help the team to a good result at Everton tomorrow," the West Ham boss wrote in his weekly column for the London Evening Standard.
"The key performance indicators were all looking good when we signed him from Ipswich this summer. Aaron had played practically every game at Tranmere before Paul Jewell took him to Ipswich, where he played 40 games-plus over the three seasons he was there.
"Our scouts and staff who watched him were all in agreement in urging us to go and get him and Ipswich manager Mick McCarthy said he was ready to take the next step. Aaron has done just that, he still has some way to go but he’s a quick learner."