A 19th minute clearance from Alessandro Nesta fell to the former Liverpool captain some 25 yards out. Redknapp shaped his body perfectly and unleashed an unstoppable volley past Luca Marchegiani and into the top left hand corner.
It was quite a way to introduce himself on his home debut.
"I wish he'd have saved it!" laughed Glenn. "It was a fantastic technique and strike - as soon as it left his foot it was in the net. That's what he can give us and it was wonderful for him in what I would call his major debut at the club.
"He's certainly going to become a favourite of the fans if he keeps striking a ball like that."
The boss was delighted with Jamie's overall performance and revealed that he did not expect him to be ready for the beginning of the season.
"I think he proved that the real Jamie Redknapp is still in there waiting to come out. His goal was magnificent and I think he played extremely well.
"I never expected Jamie to be ready for the start of the season, this is a building process, similar to what we did with Darren Anderton last year. But he proved to everyone, which is great, that the real Jamie will come out in time. I was pleased with him today."
Glenn went on to explain the care that will be taken in bringing Jamie back to full fitness and says communication is a major part.
"You just have to manage people inbetween times, there are certain techniques that we do and a lot of that is talking to the lad, sitting him down and explaining exactly what we need, what we need to protect him.
"We need feedback, sometimes players don't tell you, they have to be open and honest then you have a chance of managing them correctly. If it needs him to do a bike session or a gym session instead of training after a game you just need to manage it correctly and nurse him back to a certain position.
"Then you have to go pretty hard with him mentally through that last barrier. I've done it with many players and gone through it as a player myself and you learn from it. I'm sure Jamie's going to get there in the end.
"He's very receptive, Jamie, he's a smashing lad. He hasn't deserved the cards that he's been dealt and I just feel that the next three years might just be a fruitful time for Jamie Redknapp.
"At the end of the day I just feel we can get the best out of him again. He's going to get his knocks and bruises like any other player - we've just got to make sure he doesn't get anything long-term."
Glenn was positively purring post-match over the Jamie Redknapp strike that illuminated the Lane in Sunday's entertaining friendly against Lazio, but joked that he wished the midfield new boy had saved it a week.