Cech had just returned to training after an ankle problem kept him out for a month, while he wears a protective cap as a result of the fractured skull he sustained last season.
English told Chelsea TV: "It was only the second training session since he got back, he's looking good, looking sharp.
"Whether (manager) Avram (Grant) would have selected him to play Fenerbahce I'm not sure but he was available.
"It's just the incredible luck the guy has. But in the end it's a flesh wound and he's going to make a full recovery."
Cech is expected to be fit to play again in two weeks and English explained it is the nature of the 25-year-old's wound that is keeping him on the sidelines.
"Where Petr had his cut, from his lip going down towards his jaw, it was in a vulnerable area and you also have to think from an aesthetic point of view.
"If that wound doesn't heal well or it broke down again you could end up with a more ugly-looking scar and Petr has to look at that scar for the rest of his life.
"But he's always committed, he's a very professional player and as soon as he feels he's got the go-ahead from the medical team I'm sure he'll be extremely positive about it."