Everton suffered a 2-0 defeat to Arsenal at Goodison Park in the Premier League on Saturday afternoon.
The Toffees headed into the game against the Gunners on the back of a 2-0 victory over Chelsea at home in the quarter-finals of the FA Cup.
Roberto Martinez’s side’s performance against the Blues was brilliant, but they failed to maintain that level against Arsenal.
Former Everton star Kilbane suggested that the Toffees are suffering from inconsistency.
"It seems to be the same with Everton, one step forward, two steps back,” said on the former Republic of Ireland international on BBC Radio 5 live on Saturday afternoon (14:40).
“Great result last weekend against Chelsea, getting themselves to a cup semi-final but today it's been the same old Everton.
"Wide open, poor defensively and it's been fairly comfortable for Arsenal. Arsenal have fully deserved to win this game.”
One of Everton’s main problems this season has been lack of consistency.
The Toffees have a very good squad and some genuinely talented players, but it seems that they simply cannot perform week after week.
The Premier League season is virtually over for Everton, but the Merseyside outfit could win the FA Cup as they have qualified for the semi-finals of the prestigious competition.