"It was a big blow to miss Michael Carrick, he very much links the play for us," says Glenn.
"He can get on the ball and play short passes and long passes and is a terrific foil, particularly for Joe, allowing him to play a little bit more advanced.
"They are so different in their styles of play that they complement each other, but he wouldn't have lasted the game and he is far too a valuable member of the team to risk him breaking down."
The last game Michael missed was the defeat at Arsenal in January, and Glenn is hoping that he will not sustain any further injuries in the rest of the campaign.
"We are just hoping that patience will pay off by having him fit for the remainder of the season," he says.
"It is Tuesday today and I am as confident as I can be that he will return, but until I have seen him train and work, which he is not going to do until later in the week, we won't know.
"But he has certainly improved in the last three days - so let's hope he improves further in the next two or three days."
Another midfielder, Steve Lomas, did start the game at St. Mary's in the wake of international football, but only lasted until half time.
Of his progress, Glenn says: "Although Steve didn't pick up a specific injury, his last two games had left him feeling very tired and very stiff, particularly in his left side up around his hip.
"Again the scan revealed no problem, and we just hope that stiffness comes out by Thursday or Friday."
Glenn insists he is not dwelling on the fact that Bolton and Leeds both pulled away from the Hammers with good wins, and says: "What can we do? You can make yourself miserable about that, but there is no point - we can't do anything about it.
"Bolton are on a terrific run at the moment and they have been winning, but there is no influence we at West Ham can have over that.
"They have got a tough away game at Chelsea next week and we are at home to Aston Villa - in its own way a very tough game for us - and they can ill afford to come to Upton Park and be beaten.
"But it is down to us to keep this run going - we have three wins and two draws, and we want to keep unbeaten right until the end of the season.
"Hopefully, if we can do that, we will gather enough points."