Three of the clubs either sold infrastructure to directly linked companies, or players to associated teams.
This was previously admissible under Premier League rules - it will not be from next season - but not by Uefa regulations.
Chelsea sold Mathis Amougou to Strasbourg for £12m, while Aston Villa sold their women's team.
Newcastle posted a £34.7m profit after selling the leasehold to St James' Park and adjacent land to PZ Holdings Limited, a subsidiary company.
Last summer, Chelsea were fined 31m euros (£26.7m) for breaches of the financial sustainability regulations, with the threat of further punishments over the next three years worth a potential 60m euros (£51.7m).
Chelsea said in a statement that Uefa had "recognised the improving trend" in their spending and that the 70% threshold was only "narrowly exceeded".
All four clubs were in Europe last season, and the fines show the difficulties of complying with different rules across two competitions.
Uefa reduced the squad-cost limit from 80% to 70% of a club's income last season, making it more challenging to comply.
The Premier League has introduced its own variation of squad-cost limits, which kicks in from Wednesday.
While clubs in Europe will have to adhere to Uefa's 70%, the other 11 Premier League teams will be permitted to spend upwards of 85% of income on the playing staff and the manager.
The Premier League is trying to protect the competitive balance by allowing those without income from European competition to spend a higher proportion of their earnings.
But Chelsea, Newcastle and Nottingham Forest must continue to comply with the Uefa regulations even though they do not have European football next season.