The Tigers moved to within six points of sixth-placed Watford with a hard-fought derby win over nine-man Barnsley at the KC Stadium.
A controversial penalty won and converted by Matty Fryatt and a stoppage-time strike from Robert Koren extended Hull's impressive recent run to just one defeat in 11 league outings.
The manner of the win may not have been overly convincing with neither side excelling in a scrappy encounter.
But Mclean, making his home debut following a 1.3m move from Peterborough United, believes Hull are in fine shape to force their way into the promotion race.
He said: "We are now in the top half of the table and that gives everyone confidence throughout the club.
"We want to be in the play-offs. We got a good three points at Portsmouth (on January 3) and have now followed it up with a win at the KC.
"Getting in the play-offs is definitely achievable. We know if we put a good run together, we have got a great chance.
"It is a tight league this year, so the team that puts a run together will be the team that ends up in the play-offs.
"At the moment, we are on a decent run, so hopefully it can continue."
Mclean spent last year in the Championship with Peterborough so knows all about the teams who stand between Hull and a possible tilt at the top six.
He added: "There is nothing to fear. There are some good footballing teams and some good individual players but we know that as long as we stay together and keep a good team spirit, then we will get things from games."
Hull's revival will be put to the test in the coming weeks with their next three games being against sides involved in the promotion race.
After travelling to seventh-placed Reading on Saturday,
Nigel Pearson's men host leaders QPR and then Leeds United in back-to-back home games.
It means the coming 15 days are likely to prove an acid test of Hull's promotion credentials, a point Mclean acknowledges.
He said: "It will tell us a lot, definitely. They are good teams. They will be hard games but as long as we apply ourselves in the right way and show the same attitude and desire as we did against Barnsley then we will get something out of them."
Saturday's win over Mark Robins's men hinged on a controversial decision by referee Peter Quinn to award the home side a penalty when Stephen Foster was adjudged to have tugged at Fryatt's shirt.
With the Tigers striker being through on goal at the time, Foster was shown a red card.
Fryatt then converted the penalty to set Hull on their way to a victory that was sealed by Koren after Barnsley had been reduced to nine men courtesy of Jason Shackell's second booking of the afternoon.
Quinn's performance, which manager Nigel Pearson admitted had been "inconsistent", left Reds manager Robins incensed but the Hull players felt the official had got the penalty award right.
Mclean said: "I didn't really see it (the penalty incident). I had dropped a little bit deeper on a quick throw-in and Matty had got in behind them.
"But from what all the lads were saying, it was definitely a penalty."
Robins, however, took a different view on the 66th-minute incident that he felt totally changed the course of the game.
The Barnsley manager said: "It looked like Steve had stepped the wrong side and it looked like he was being held.
"The challenge was a 50-50 that went the opposition's way. Then he sent him off and from then on we are trying to get back into the game.
"It was the turning point of the game. If that is a penalty, there probably should have been six or seven penalties. There was plenty of pulling in both boxes.
"He (Quinn) was a first time Championship referee and he has cost us at least a point."
Robins was also unhappy about the red card shown to Shackell, which came after the defender appeared to kick out at Anthony Gerrard in stoppage time.
He said: "Thirty seconds before the second red card, there was a tackle by Nolberto Solano (on Adam Hammill) that was overlooked.
"It is disappointing for us. Not only do we lose this game, but we lose both our centre-halves against Swansea. They have played every minute of every game. "I felt we were worth a point."
Hammill's future continues to be the subject of much speculation amid interest from a host of Premier League teams.
A 500,000 buyout clause inserted in the Barnsley wideman's contract means he is unlikely to remain at Oakwell for too much longer, a feeling only strengthened by Hammill throwing his shirt into the away end at the final whistle on Saturday.
Asked about the gesture's significance, the Reds manager replied: "I have no idea. The significance is it will cost him 100."
On the future of Barnsley's prize asset, Robins added: "There has been a lot of speculation surrounding one of our players and it is having a detrimental effect on his performances.
"That situation needs resolving pretty quickly. We need to move on and move forward."
Hull, meanwhile, are understood to be giving a trial to 23-year-old Tunisian midfielder Tijani Belaid, who recently left Slavia Prague.
Leeds will go into their FA Cup third-round replay with Arsenal in tremendous heart after goals from Sanchez Watt, Max Gradel, Bradley Johnson and Davide Somma condemned struggling Scunthorpe to a 4-0 defeat.
Leeds are now level on points in fifth place with Cardiff and Norwich.
Middlesbrough won by the same score as Leeds, former Bristol City striker Leroy Lita scoring two goals and making one for Boro on a memorable return to his old club.
Lita forced the opening goal just before half-time, his low cross being deflected into his own net by defender Kalifa Cisse.
Lita headed the second past David James from close range and Barry Robson (76) grabbed the third.
Former England goalkeeper James was sent off in the final minutes for tripping substitute Cameron Park and Lita hammered home the resulting penalty, defender Liam Fontaine having taken over the goalkeeping duties as Bristol City had used all three substitutes.
Doncaster Rovers went down 3-0 at home to Reading, Shane Long, Jimmy Kebe and Jobi McAnuff getting the goals, and new manager Micky Adams saw his Sheffield United side draw 0-0 at Coventry.