Everton lost 1-0 away at Watford on Saturday evening.
The Toffees travelled to Vicarage Road on Saturday night to take on Javi Gracia's Hornets, and were hoping for a positive result, two weeks on from their last game; a 3-1 home win over Crystal Palace.
However, Allardyce's men served up another dismal away showing, and appeared to be heading for a fairly mundane 0-0 draw before suffering a sting in the tail late in the day in Hertfordshire.
Troy Deeney struck late on to hand Watford a 1-0 victory, with Everton paying the price after Michael Keane and Oumar Niasse squandered chances to score for the Toffees.
Another player who had a chance to find the net was striker Cenk Tosun, whose header tested goalkeeper Orestis Karnezis as the Turkish international came off the bench to try and aid the search for an Everton goal.
The January signing from Besiktas – who hit 14 goals in 24 games earlier this season – hasn't enjoyed the greatest start to life in English football, and was making just his fourth appearance under Allardyce, his second in a row as a substitute.
The 26-year-old is still searching for his first Everton goal amid claims that he hasn't adjusted to life in English football just yet, but he did get a 33-minute run out against Watford in place of Niasse.
After the game, manager Allardyce has told Sky Sports that he hopes to see Tosun improving after his cameo, calling on him to provide what Everton are really lacking away from home right now; goals.
"Hopefully that will improve and he will end up doing what we need. Score goals, particularly away from home," said Allardyce.