"I have a lot of trouble with the players taking on to the pitch what we asked them to do", Allardyce told the BBC.
In the aftermath of the match, Allardyce lashed out at "unacceptable" performance from his players, calling his side's display 'pathetic'.
Walcott already scored a brace in the Merseyside club's 2-1 win over Leicester City in the last league tie.
"I think a lot of negotiation was done by Theo: Because of his service to the club and the fact he would accept what Arsene was doing - he is not a troublesome player who would throw the toys out of the pram - that respect between him and the club resulted in the move", Everton manager stressed.
However, Everton have won only one of nine matches in all competitions since, scoring five goals.
However, Everton lacked discipline, with new loan signing Eliaquim Mangala - signed on loan from Manchester City on transfer deadline day - enduring a terrible debut. Obviously we didn't put that game plan in the manner Swansea put it in.
"These were clear instructions today, because there was a very, very good performance by Swansea on Tuesday against Arsenal that made them a very, very good victory".
Everton have improved since Allardyce took charge but a 5-1 thumping away to Walcott's former club Arsenal has hindered their charge.
"We set out to play like [Swansea], but unfortunately Swansea played at the top of their game and we played at the bottom of our game, which is to say that any tactics and any system you pick is absolutely worthless if your players don't play to their best".
"It's about being able to nullify the strengths of Arsenal and then, I've always felt, that defensively they are weak because of the amount of players they commit forward". Everton were all over the place.
Everton were staring down the barrel at half-time, with Allardyce's men looking stunned by the pace and precision of Arsenal.
"They were embarrassing. They were hopeless defensively in the first 45 minutes".