They were twice denied by goalline clearances after just seven minutes when first Samuel Di Carmine thundered a shot but Brendan Moloney cleared off the line, before Alberti struck the rebound but Joe Heath produced a stunning block again on the line to save the Reds.
A clash of heads left striker Nathan Tyson with a nasty gash and he had to go off after 15 minutes to further deplete the Forest side.
Skipper for the day Wes Morgan offered a header wide from a corner before Alberti struck a shot on the turn from inside the box only to be denied by the upright.
Despite dominating the opening period, QPR found themselves behind when Matteo Alberti brought down Luke Chambers in the visitors box and Lewis McGugan converted the resulting spot-kick.
Alberti made amends a minute later, when he converted with the last kick of the half, after good work down the right by Matthew Connolly. Three minutes after the break, the little Italian calmly buried his second into the top corner after a clever flick by Wayne Routledge.
Routledge should have made it three when he flicked the ball over the head of Heath down the right of the box but pulled his shot wide of the far post.
But Rangers were pegged back mid-way through the second half, when Luke Chambers, who was fantastic for the home side, caught the visitors napping with a teasing cross that Chris Cohen nodded into the back of the net.
Mikele Leigertwood thought he had put QPR ahead again when meeting a corner from the right only to be denied by a stunning save from Smith.
Routledge and Mahon also went close for Rangers, who had ten attempts on goal to Forest's five, as well as the lions' share of possesion.
Matteo Alberti, who was a surprise inclusion, was in the thick of the action this afternoon, while Samuel Di Carmine was preferred to top scorer Dexter Blackstock in attack, after Heider Helguson picked up a knock in training during the week.
Rangers have now dropped to ninth in the Championship table, after Swansea City and Bristol City both won today, but they remain three points off Preston, who remain in sixth place after a stalemate against Reading.
Ipswich Town are up next for QPR, in two weeks at Loftus Road. They lost 3-0 to Swansea this afternoon, but lie just four points behind Rangers in the table. The Super Hoops will be looking to avenge the 2-0 defeat at Portman Road earlier in the season.