The Toffees face Norwich City in the fourth round of the Capital One Cup on Tuesday evening, with a place in the quarter finals up for grabs.
The FA Cup in 1995 was the last major piece of silverware that the Blues secured for their trophy cabinet, whilst the League Cup has continued to evade them at every turn.
And midfielder Barkley, who scored in the 2-1 defeat to Arsenal last Saturday, claims it is time that statistic changed.
“That’s our aim,” the 21 year old said when asked if Everton could lift the cup this year.
“We haven’t won anything for a while and we’ve had a couple of good results in the competition so far and hopefully we get the result against Norwich that will put us through to the next round.
“It’s about getting it going on Tuesday night, getting the crowd behind us and our focus is going into that game lively.
“We want to get a few goals and give ourselves a bit of confidence.”