"There has been a furore over the incident which has probably gone too far and we would like to draw a line under it now and let Martin get on with his career and hope Eduardo gets back as soon as possible," McLeish told Sky Sports.
"I think Martin's wife was upset at the weekend but he has come in this morning and got on with his life again thanks to the support of everyone who knew it wasn't a challenge with malicious intending to injure a player.
"We've had to rally around Martin because he was mentally shattered by the whole experience. I would have been worried about him coming into training today had we not received the support from football people the length and breadth of the country.
"But the fact he has had such magnificent support has helped Martin psychologically because I felt he could be damaged by this incident as well.
"We have shown as a club we are right behind the big fellow. We have rallied around him, got him back into training. It was important he did that as soon as possible."
Gunners boss Arsene Wenger retracted his post-match statement about Taylor whom he claimed "should never play football again."
McLeish said: "The fact Arsene has retracted them tells you the whole story. I did say after the game that maybe Arsene has acted in the heat of the moment and Arsene admitted he had done that.
"We've got to let that lie now, move forward and Martin has got to get on with his football career again and we are all right behind the big fellow 100 per cent and we are very gutted for him and Eduardo."
McLeish admitted that Taylor may have been unable to continue during Saturday's game had he not been given a red card by referee Mike Dean after the third minute incident.
He added: "Martin was horrified and, if the referee had given him only a yellow card rather than a red one, I don't know if he could have played on anyway. You just had to see the look on his face.
"He was horrified and it affected our players as well as the Arsenal ones. You've got to move on but it was certainly an horrendous injury and some of the players were horrified by what they had seen.
"I've seen similar injuries. Henrik Larsson had one for Celtic against Lyon and I could only think it is something similar to that.
"Henrik came back from that and showed he was a world class player. Eduardo is a world class player and he is definitely in the right hands and I am sure he will come back."