The Gloucester flanker was shown the yellow card by after a trip on Falcons number 10 Jimmy Gopperth, who kicked four penalties and two conversions as Newcastle came back from 20-10 down to edge home in Friday night's Aviva Premiership clash at Kingston Park.
James Fitzpatrick crossed for a converted try just a minute after Strokosch's 32nd-minute departure and Gopperth added further punishment with a penalty a minute after half-time.
"The trip was the turning point of the game, there's no doubt about that," said the Gloucester head coach. "We weren't under any real pressure but we went from 20-10 to 20-17.
"The players have to take a long hard look at themselves. There is bound to be some criticism about the way we have been losing tight games and there's no hiding from that.
"Our set-piece was poor, our basic skills were poor and so was our discipline - if you give Jimmy Gopperth five shots at goal, he is going to take most of them."
Redpath's opposite number Alan Tait was largely in agreement and said: "The yellow card was something of a turning point but I'm not surprised. We had a review of the refereeing after the Harlequins game and it was quite clear that Jimmy is a target and needs to be protected.
"We took 10 points while Strokosch was in the sin-bin and that proves how important yellow cards are in the game."
Tait added: "It was not the best of starts by us and I thought 'here we go again' when we gifted them two tries, but you have to give the players credit for the fightback and they really grafted for the win."
The Falcons' victory cuts the gap between them and second-bottom Worcester to just five points and Tait added: "Five points is nothing and I'm a lot happier now.
"I'm licking my lips now for the rest of the season because we have a real spirit and now real competition for places."
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