Tottenham have been the Premier League big spenders this summer, outlaying over £100m in transfer fees.
And Barnet player-manager Davids believes Eriksen could be a shrewd acquisition for Spurs, who he thinks must now qualify for the Champions League next season.
"There is now a lot of pressure because now they cannot come fifth," said the former Champions League winner.
"If Eriksen can do what he has been doing with Ajax, and do what he does best, he is going to be a bargain and it's going to be a very good season for Tottenham."
Eriksen was just one of a trio of signings for the north London side on Friday, following the arrivals of winger Erik Lamela and defender Vlad Chiriches earlier in the day.
Tottenham sold prized asset Gareth Bale on Deadline Day for a world-record fee reported to be in the region of £85m.
They have raised a further £23m through the sales of Steven Caulker, Clint Dempsey, Tom Huddlestone and Scott Parker.
The club have recorded a profit on their summer transfer dealings as a result, and Davids believes that Tottenham's transfer strategy will benefit the club and manager Andre Villas-Boas going forward.
"Tottenham have done well even if Bale has gone," said the former Juventus and Barcelona midfielder.
"I think last season they depended too much on Bale and if you depend so much on one person then it is only a matter of time until you need to adjust your system.
"If your system is based on one player, I don't think it is a strong asset.
"Now with six or seven new good players instead he will have a more balanced team I hope."