"Wales were disappointing and it is going to be a big week for them with so much still to be achieved," said McGeechan.
"The Springboks played very positive rugby and they really got tempo into their game. Wales will have to ensure they don't give away as much turn-over ball or in the second Test.
"I had a chat with Warren Gatland and Shaun before the game and I'll be catching up with them again during the week."
Edwards, who is Gatland's assistant coach, is backing the Welsh players to cast aside their "rusty" performance in the first Test and give the Springboks a better challenge at Loftus Versfeld on Saturday.
The world champions put four big dents in Wales' much vaunted defensive system in Bloemfontein as they ran in twice as many tries in 80 minutes as Wales had conceded 400 during the 2008 Six Nations championship.
"We'd like to think we can get more respect. I would like to think that we can give them a better game next week, although whether we beat them is a different issue," said Edwards.
"The fact that the players had not played for five weeks was an issue going into the game. We have to be honest, we looked very rusty.
"They are the world champions and the one thing that South African rugby always has is amazing physicality. But the one thing we didn't expect us to be doing was to drop simple passes - and when you give them 18 turnovers it makes it very difficult.
"Maybe you can do that against an average team but when you do that against the world champions in their own backyard you are going to commit suicide. We need to sort out the line-out and there are a couple of issues with the defence.
"Five weeks off has not done us any good at all, but I'd like to think we can give better accounts of ourselves next week. The encouraging thing for me is that we play them again on Saturday."
Welsh try scorer Shane Williams, who side-stepped his way to his 42nd Test try in the second half, said he was angered by the poor performance by the Grand Slam champions.
"It was very disappointing - an atrocious performance. We have trained really well over the past few weeks and we just let ourselves down," he said.
"We just did not play like we know we can. We knew South Africa would be very physical but we have worked really hard in training and the gym and felt that we would be able to compete.
"We just could not hold on to the ball and gave them too many turnovers. I wouldn't say we were humiliated, but I am very angry at the performance.
"We just did not play like we did in the Six Nations. We are a better side than that and need to show it next week."