Lammens was outstanding on Monday night for the 1-0 win.
Carrick won the Champions League with Van der Sar and said: "I definitely see the similarities, without comparing them. I don't want to be comparing them because I don't think it's fair to Senne. But there's definitely similarities.
"For me, he's a goalkeeper to be reliable, be trustworthy. Instead of creating chaos, you want him to take the chaos away and calm things down. I think Senne is that. He's quite quiet at times and unassuming, but he's got a real steel.
"How he's gone about it at the moment is with calmness, with composure. I think it does help those in front of him an awful lot."
Carrick added, "A major part of it is the character and the personality, and that is a major attribute to have, especially playing here, so Senne kind of.
"The jump that he's had is a big jump, no disrespect. It's a huge jump for the one he made and to take it like he has done and just get on with things speaks volumes of his personality, and he's able to just deal with the environment and play at that level.
"Listen, that was a tough place, that last 15 minutes, the amount of crosses and corners and things that he had to deal with and a couple of shots that he just catches and takes the sting out of it. So to be able to do that in such a manner is obviously pleasing for us."