Sam Allardyce felt the Southampton midfielder should have been sent off by referee Andre Marriner for 33rd-minute tackle on Diame which the West Ham boss insisted was a "two-footed challenge".
Marriner did not even award a free-kick for the tackle, and Schneiderlin insisted there he had not committed a poor challenge.
"I need to see the image again but at that moment I didn't think I had done anything wrong," the Frenchman told Sky Sports 1.
"I didn't have the feeling at the time that it was bad, I am not a player who commits those kind of fouls.
"If I touched him in any way I apologise but I have not the feeling that I did anything wrong."
Of the 0-0 draw, in which Jussi Jaaskelainen denied Saints with a string of fine saves, Schneiderlin said: "We had three or four very clear chances and their goalkeeper made some very good saves.
"It is very hard to take because we had the feeling that we did everything to win that game.
"West Ham had one or two chances but other than that, they didn't create anything else so we felt like we should have won the game.
"It's disappointing because in our two home games so far we've done everything to try and win the game.
"We had a good first result at West Brom but haven't really built on that. Now it is up to us. Next week we have a very hard game at Anfield so hopefully we can improve this week and score some goals."
Southampton boss Mauricio Pochettino also felt his side deserved to win, saying: "We created the better chances, we were much closer than they were to actually getting a victory today.
"But in football, it is not just about creating chances, you need to be make them into goals. Today we weren't able to do it and we are frustrated by that.
"I am pleased with all of my players - they all played well and put in a great effort today.
"On the one hand, I am a bit frustrated because we didn't get the three points but I'm pleased, as they all played well today."
Considering Southampton's abundance of attacking options, their lack of goals this campaign has been frustrating for Pochettino.
Dani Osvaldo has yet to find the net since his club-record move from Roma, while Rickie Lambert has yet to replicate the fine form he has shown for England.
"He has played the last two with national side, which must be a huge boost for his self-confidence," Pochettino said of Lambert. "At the same time strikers need to score goals, that is their bread and butter.
"He hasn't been able to do that, none of them were able to do that, so I'm frustrated.
"We created many chances today and on another day those chances might be goals."