Wanderers.Mandron handed the visitors the lead before Delfouneso equalised before half-time, before Finney and Kirk struck after the break to make it 3-1, before the Bolton striker scored his second of the game.
The Gresty Road side had lost their previous three matches heading into the clash at the University of Bolton Stadium 1-0, losing to Lincoln City, Ipswich Town and Gillingham.
And Artell believes the result against Ian Evatt's side is the worst his side have played of late, despite ending up with a victory and a place in the second round.
He insisted he always felt comfortable in the tie, but was disappointed the Railwaymen gave the Trotters a glimmer with Delfouneso's second goal to reduce the deficit not long after Kirk's effort.
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