QPR hit back from conceding two goals to Bowen to earn a share of the points courtesy of second-half strikes from Josh Scowen and Tomer Hemed.
QPR manager McClaren said: “We couldn’t cope with the boy Bowen. What a good player. He was always a threat.
“You know he is coming in on his left foot and there is nothing you can do about it. They have got a real gem in him.”
Bowen took his tally for the season to 21 goals as he struck early and late in the first half with two almost identical shots, cutting in from the left to fire into the far corner.
He almost grabbed his hat-trick just before the hour but for once Bowen fluffed his lines. The winger missed his kick and the ball fell to Fraizer Campbell whose shot was blocked on the line by Joel Lynch.
It proved costly for the Tigers as the visitors were back in the game shortly afterwards as substitute Scowen beat Marshall with a scuffed effort into the corner.
Reece Burke did well to block a shot from Wells and from the resulting corner Marc Pugh headed off the line from Scowen.
Just as it looked like Hull had done enough to secure the win, QPR equalised with six minutes to go.
Substitute Hemed poked home from close range four minutes after coming on after Scowen had cut the ball back to ensure the points were shared.
While Bowen impressed McClaren, the winger also drew praise from Adkins, who said: “We got off to a great start with a great goal from Jarrod.”
Adkins was not happy with either goal his team conceded but felt his players were let down by the officials. “We had said before the game how important it was to go and win it,” added Adkins.
“The first goal should have seen a free-kick awarded in the build-up. He side-foots it in from 35 yards and we have got to stop that.
“With the second goal, the ball had gone out but the linesman could not see it because he was not up with play. Our centre-half was appealing for it and their player scores.
“I am so frustrated that we put ourselves in a position to win the game and we have only got a point.”
The result left Adkins’s side in 12th place and six points outside of the play-offs with eight games remaining and several other rivals having games in hand.
Hull City: Marshall, McKenzie, Burke, Ridgewell, Kingsley, Bowen, Stewart, Irvine, Grosicki, Pugh, Campbell (Martin 77). Unused substitutes: Lichaj, Evandro, Dicko, Milinkovic, Long, Kane.
Queens Park Rangers: Lumley, Furlong, Leistner, Lynch, Bidwell, Wszolek, Cameron (Scowen 56), Luongo, Freeman (Samuel 46), Eze, Wells (Hemed 79). Unused substitutes: Ingram, Hall, Cousins, Manning.
Referee: S Martin (Staffordshire).