Mark McCall admitted he was "proud and thrilled" after Saracens' memorable triumph over adversity against Ospreys in Swansea.
Saracens' 22-15 Heineken Champions Cup victory kept alive their quarter-final hopes, and it was achieved despite having Wales international prop Rhys Carre sent off in the fifth minute.
They even went down to 13 men for a spell when flanker Calum Clark was sin-binned, but 17 points from teenage fly-half Manu Vunipola and an Alex Lewington try saw them home.
It means they are likely to reach the last eight for a ninth successive season by beating Allianz Park visitors Racing 92 next weekend.
Saracens arrived at the Liberty Stadium after a week when lawyer Neil Golding was appointed as non-executive chairman, succeeding Nigel Wray, while it also emerged that players are set to be trimmed from a star-studded squad in order to comply with salary cap regulations.
Saracens were docked 35 Gallagher Premiership points and fined £5.36million after being found to have exceeded the £7million salary cap limit for the past three seasons.
"We were down to 14 men for virtually the whole match, really, and the way the players problem solved all the way through the game was outstanding," said Saracens rugby director McCall, who rested the likes of Owen Farrell, Jamie George and Maro Itoje.
"Our senior players - Jackson Wray, Richard Wigglesworth, George Kruis - were magnificent out there in coming up with the right answers to solve the problems.
"And our younger players listened to what they said and got stuck in and displayed an incredible amount of energy. It was a great energy."
On the red card, awarded following a shoulder-led hit to Ospreys full-back Dan Evans' head, McCall added: "I haven't had a really close look at it.
"If the referee said it was a head contact, you are going to face the consequences, but I haven't seen it closely enough."
McCall, meanwhile, paid tribute to former England scrum-half Wigglesworth following a masterful display that showcased all his experience.
"He was amazing," McCall said.
"He's 36 years old, and in situations like that you need to have somebody with that kind of experience to play the game at the pace you need to play at with 14 men.
"The players stuck at it. The forwards delivered massively, particularly in the second half, and got the job done.
"The thing we talked about the moment the (salary cap) decision was made early in November was that we wanted as a staff and as a group of players to show unity all the way through when we had a chance to play and show togetherness.
"Today was all about togetherness and listening to the senior players and doing it for each other. The performance spoke volumes.
"I am just so proud and thrilled with how the players coped with a very difficult situation today. There is a real spirit in this team."
And skipper Wray said: "I am unbelievably proud. The forwards stepped up and took a lot of the load once that red card came.
"We controlled the pace really well and got some dominance up front. It was about working hard and working smart to not give them edges or holes through the middle."
Evans scored two tries while Clark was off, with fly-half Luke Price adding a penalty and conversion, but the Ospreys ultimately suffered a fifth successive European defeat this season.
Ospreys forwards coach Carl Hogg said: "I think we missed out on a golden opportunity. Saracens went down to 14, and we had an opportunity to win a game of rugby.
"I thought our discipline in the first half allowed them to get a foothold in the game and build a lead, but I still think we had chances.
"I think we were architects of our own downfall in that first half."
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