Assistant head coach Andy Crosby played down Hull's chances of reaching the play-offs after the 6-0 victory at home to Bolton.
Nigel Adkins' side were in the bottom three of the Sky Bet Championship at the start of December.
But they have now won their last five games and are, remarkably, seven points away from the play-off places.
Crosby said: "If anyone's talking about the play-offs they'd probably have the manager all over them.
"Who knows what the future holds. We didn't get too down when we were down at the bottom of the table. Slowly but surely, things have turned.
"We've got to keep pushing. We've got good players who are playing with belief, but we've got to keep taking things one game at a time. It's important we keep developing.
"We are looking up now. Can we keep progressing and go higher up the league?"
Man-of-the-match Kamil Grosicki offered a glimpse of what was to come when he thumped Hull into a 29th-minute lead from a tight angle.
Bolton had at least been competitive in the first half, but they fell apart once Evandro made it 2-0 after 62 minutes.
Grosicki's curling hit from distance 60 seconds later confirmed another Hull victory, while Chris Martin, Jarrod Bowen and substitute Nouha Dicko turned the match into a walkover.
Crosby added: "We were very wary of the threat of Bolton.
"It was important we got the first goal. They were a threat, but we managed to take the game away from them.
"In the last half an hour you saw a team playing with confidence.
"We probably could have even scored a couple more – that's belief and confidence in each other.
"The club has perhaps been on a downward spiral for a few years, but hopefully we've turned a corner and hopefully we can continue to ride this wave and progress up the table."
Bolton manager Phil Parkinson admitted personal responsibility for the severity of the scoreline.
Parkinson substituted Marc Wilson, who was suffering with a thigh strain, for the more-attack-minded Erhun Oztumer at half-time.
His team conceded five goals after the interval and never once tested Hull goalkeeper David Marshall.
Bolton are now three points away from safety and Parkinson said: "We were in the game in the first half.
"But we got really exposed by a team that is full of confidence and have some outstanding attack players.
"We haven't really been turned over like that (this season), and I've got to take responsibility for that as I opened the team up at half-time.
"We made some strange decisions at 3-0 and 4-0 down but they were very clinical when the chances came – and that was the difference.
"We looked like a team that ran out of legs."
