United goalkeeper Jamal Blackman was named man of the match in the 0-0 draw - Karanka knows the Chelsea loanee well, having worked with him at Middlesbrough - and the City Ground boss said: “We need to play attacking with the same aggression as when we are defending, because with these players we will win more games.
"I think we deserved three points. The best example is that man of the match was the keeper (Blackman)."
The hosts' top-scorer Leon Clarke had the pick of the chances in the first half but he unbelievably missed the target with a header from inside the six-yard box.
United pushed on in an attempt to grab all three points and Forest countered them several times but on-loan Chelsea goalkeeper Blackman pulled off some eye-catching saves to deny Kieran Dowell, Daryl Murphy and Ben Brereton.
"I think the last few weeks now, we look like a proper team,” Karanka added.
"We are really consistent, we are a team on the pitch and now that's another step, but we had a lot of chances to score today, especially in the second half.
"We score those chances and we will win a lot of games. We need to keep going, keep improving.”
Karanka’s opposite number Chris Wilder, whose side are two points off a Championship play-off place, admitted: "We didn't deserve to win it. We didn't show enough quality in the final third and when we did, we've missed chances.
"First goal is massive, especially with our record when we've gone in front here, which is pretty good. I think we've won all our home games when we've scored first so, yeah, it was a bit frustrating.”