Walcott scored twice against Leicester in just his second game for Everton but has failed to net in his subsequent five matches, and saw an effort ruled as an own goal on Saturday.
That was a week after the Turkey striker, signed in January from Besiktas for a reported fee of £27million, opened his Everton account at Burnley.
Allardyce said: "The second goal was why we brought Cenk into the club".
"As a manager and a coach, you try to raise your players for every game but it's very hard against good opposition". "We all felt it, I think you do". We have been really good at Goodison but we know we have to be better away.
"But also we have been missing for far too long Seamus Coleman, Leighton Baines, Yannick Bolasie".
But any hope Chris Hughton had of his side springing a surprise comeback was largely ended when Anthony Knockaert was shown a straight red card for an ugly, two-footed lunge on Baines.
He told Sky Sports: "It was [a bad day at the office], if we play at a level like that, we will find it hard to win any Premier League games".
'We were already picking a very attacking side, so we said we'll go and sit Wayne Rooney in the middle where Gana would sit and get him on the ball and produce and see how it goes and what a masterful job he did for me today'.
Brighton remain seven points clear of the relegation zone, but they must still face all of the current top four before the end of the season.
"In the first half we played well but didn't score".
"As a manager you try to raise your players for every game, and it's very hard when you are playing against good opposition".
"I think with what Everton have, the first goal was going to be important and it turned out to be", Hughton continued.