Cpl Mike French, 34, was performing at the Whitehaven Air Show in Cumbria on Friday when the accident happened.
His parachute wrapped around Cpl Wayne Shorthouse but they managed to land in the harbour.
Cpl Shorthouse, 32, said he was no hero and both men had been trained for such a scenario.
Cpl French said the plan had been for his parachute to be caught by Cpl Shorthouse as the first stage of building a formation.
"As soon as I had made contact with Wayne from the back, I looked up and saw the parachute was a little bit wrapped around," said Cpl French.
"It was pretty much straight away you realise it's not exactly how we planned to do it but then training kicks in and members of the Parachute Regiment, the British Army, we always train for every eventuality.
"Display parachuting and especially canopy formation within display parachuting is a very difficult and dangerous aspect of sky diving so constant training is one of the things that kept us [safe], the communication and Wayne having a good parachute above his head."
Asked if he could repay his colleague, Cpl French said: "A pint of beer maybe."
Cpl Shorthouse, however, said he was "just doing his job".
Both men said they were looking forward to the next display.
Onlookers at the display said the dramatic scenes had caused panic among the crowd with one describing the event as "frightening".
Lucy Milne, who was watching the display, said: "It seemed to go on for ages and it's just seeing the panic of everyone around you and seeing it on the parachute guys as well  - the panic.
"And then all of a sudden he just started to go really quick and everyone was holding their breath and then all of a sudden they were in the water.
"Everyone was staring at the water for ages waiting for them both to pop up and then when eventually they did everyone clapped."
The Red Devils formed in 1963 and carries out more than 60 displays every year.
It currently comprises 12 serving soldiers from the three battalions of the Parachute Regiment, all of whom have to have at least three years experience.
A Red Devil parachutist has said he owes his colleague a pint of beer after the pair got tangled in mid-air but safely reached the ground.