A flattering 3-1 scoreline in yesterday’s third-round tie at Goodison Park secured victory for the Toffees over a League One side who deserved a replay for their efforts.
Neville singled out Donegal-born Seamus Coleman for special praise, claiming the former Sligo Rovers defender “ignited” the home side when introduced late in the game.
Carlisle boss Greg Abbott was rightly proud of his side’s display, fighting back to level through Kevan Hurst’s scuffed equaliser after Adam Clayton’s poor back-pass had gifted James Vaughan an early opener.
Had skipper Danny Livesey’s hook against the bar with 19 minutes left been a fraction lower, the Cumbrians could have been heading for glory.
They held out until the final minutes when Tim Cahill grabbed his 50th goal for Everton and teenager Kieran Agard won a stoppage-time penalty which was gratefully converted by Leighton Baines.
Neville, starting his first game since September after a serious knee injury, is hoping now for another cup run just like last season when Everton went all the way to Wembley.
He said: “Carlisle were outstanding. It was hard work, but in the end it is about being in the hat for the next round.
“They gave us a fright, hitting the bar when it was level and 3-1 totally flattered us. Our performance was not up to what it has been recently.
“But we are still in the competition. And looking back at our unbelievable cup run last season, we struggled at Macclesfield in the third round but managed a win there.
“It was a similar type of game to this one, and last season we still ended up at Wembley.
“We have a big couple of months coming up in the league, cup and Europe, and if we can come out of that in good shape we can really attack the last half of the season.”
Neville added: “As for me, I’m delighted to be back. I feel fine and really fresh. It is just a case now of hard training and building up my fitness.
“In the end it was a couple of the youngsters, Agard and Seamus Coleman, who came on and swung the game.
“In the end there were three good young lads out on the pitch. Vaughan scored our first goal, Coleman ignited us when he came on down the right and Agard won the late penalty.
“That is three plus points for us and there are plenty more youngsters here waiting for their chances.”
EVERTON: Howard, Hibbert (Coleman 80), Heitinga, Neill, Baines, Pienaar, Neville, Cahill, Fellaini, Bilyaletdinov, Vaughan (Agard 86).
CARLISLE: Collin, Keogh, Livesey, Harte, Horwood, Hurst, Clayton, Kavanagh (Anyinsah 85), Taiwo, Robson, Pericard (Dobie 77).
Referee: Jon Moss.