The Macedonia international plans to say sorry to his Albion colleagues when they return to training on Thursday, and also intends to contact Walker.
"I am disappointed after this," said Popov.
"I just want to say a big sorry to everyone, firstly to the gaffer because he was so angry after the game and, if I was in his place, I would be exactly the same, and to all the players.
"We played a good first half then at the start of the second half their player kicked the ball to the corner and I said something to him.
"We exchanged a couple of words but it wasn't something bad, just something that happens 10 to 15 times in a game.
"After that, when he started to run, he was maybe two or three yards away from me. I didn't have the intention to spit on him - but it looked like that.
"The referee was close to me and saw that. This is not good for me because over the last two or three nights I have not slept too good.
"Something like this has never happened in my life."
Walker is currently on international duty with England and Popov says he will call him to apologise.
Popov said: "When I get his number I will call him and just say 'I'm not a player like this, I didn't want to do this to him and a big sorry'."