West Brom are understood to have had a £5million bid for Marshall rejected, and he demonstrated his value with some vital saves at the City Ground.
A 23rd-minute goal from Kenwyne Jones and another from Joe Mason four minutes after the break put the visitors in control. But Marshall had also had to deny Tyler Walker twice and Michail Antonio once, with important stops, before finally having his resistance broken in the 86th minute, after Antonio had darted clear.
"It was a good away performance," Slade said. "We dominated possession and were the better team for long spells - but then caused ourselves a few problems. We should have put the game to bed.
"We go into the international break unbeaten and we knew this would be a tough game. But we acquitted ourselves really well. We have made a solid start and the performances have been good.
"First of all, you need delivery and It was a great ball in and then a great finish from Jones. Then Mason came up with a real striker's goal, just getting a great little touch on the ball to guide it home.
"We are quietly making progress and we like it that way, of course. We have made a really solid start and the performances have been good. We are getting our rewards for hard work."
As for Marshall, Slade said: "I can't see anything happening. His performance today was excellent. He had to make two or three very good saves. He kept us firmly on top.
"I have said all along that we do not want to lose our quality players - we want to keep them. And David is one of those players."
As well as the heroics of Marshall, Forest boss Dougie Freedman felt the experience of Cardiff's frontmen had been decisive.
"The difference, in a nutshell, was that they had two very good strikers, who got them goals, and an excellent keeper who kept them in the match," said Freedman, who started with teenager Tyler Walker up front - and later brought 17-year-old Gerry McDonagh off the bench for his debut.
"I cannot be disappointed in the way we are playing or in our spirit, because we gave it a go. We have a lot of young players and that was the difference today, when it came to our decision making in the opposition box.
"For most of the second half, we were knocking on the door. It was just their keeper who saved them a few times. Had we made better decisions in the final third, we might have got a better result.
"But we are working away with the younger players and don't feel sorry for me. This is where we are. We have three or four good strikers on the treatment table."