The Robins recovered from falling 12-0 down early on to post eight tries in a fine display that pushes them five points clear of their nearest rivals with four games of the regular season remaining.
"I think fourth is ours to lose now," he said.
"We spoke about that before the game. Mathematically, obviously there's a chance for us not to be fourth but we've got one hand on fourth place and we need to capitalise on it with eight points up for grabs, I'm confident that we won't lose it and that will be the first tick in the box."
Shaun Briscoe scored a hat-trick for Rovers while Peter Fox and Michael Dobson both crossed twice. Dobson's tries, coupled with his seven goals, saw him end up with 22 points to his name following a fine performance.
"He was great, I thought he showed great composure," Morgan said of the Australian who became the first player in the competition to score 200 points this season when he kicked his third conversion.
"I thought most of the time he showed a lot of maturity in leading us around the park in what types of plays to call at certain times.
"He is very young and sometimes that youthfulness means he likes to roll the dice all the time but I thought today he learned how to control the game and effectively put more pressure on the opposition."
Morgan's opposite number Terry Matterson was not too downhearted after seeing his side's four-game winning sequence come to an end.
The Tigers, chasing what would have been just a fifth home win of the season, were arguably the better side of an enthralling first half, with tries from Brett Ferres, Craig Huby and Ryan Hudson giving them a 20-18 interval advantage, before Rovers took control.
"I wouldn't call it frustrating, I think the scoreline was harsh and it was a cracking game of rugby," he said.
"What a spectacle. The endeavour from both sides was really good.
"There were a couple of things that didn't go our way. I said at 40-28 that we were going to get a draw but then Rangi (Chase) made a mistake. Credit to them, they kept coming and their kicking game was excellent. I think they just shaded us on the day.
"At half-time we could have been two or three scores up and that hurt us at the end of the game. We'll take a lot positives out of today and look forward to going to Headingley in our next game."
Hull (46) Tries: Cusack, Whiting, Washbrook, Burnet Goals: Tickle (4)
Castleford (28) Tries: Evans, Ford, Dixon Goals: Dixon (2)
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