Cunningham, on loan from Manchester City, suffered the break on 62 minutes in a challenge which earned Rosenior a red card.
Leicester manager Eriksson said: "It's a broken tibia, which could mean he is probably away for four months. He is in hospital and will undergo an operation.
"It is important to say that as far as Rosenior was concerned, it was not stupid. It was bad luck and he didn't mean to do it, so there should be no shadow over him.
Tigers boss Pearson concurred there was no malice in Rosenior's tackle on Cunningham.
"It is obviously regrettable and you never like to see players have a serious injury. We wish the player a speedy recovery," he added.
"Liam's distraught; it was just slightly mistimed with two players going for the ball. It would be wrong of me to complain about something like the red card and I have no complaints about it.
"It was very unfortunate as it didn't look ridiculously high. There was no malice in the challenge. If you know the player you'd be very aware of that."
Darius Vassell scored the winner after 10 minutes with a superb volley from 12 yards.
Pearson was disappointed with his side's performance and said: "We were second best all over and the reasons for that are difficult to isolate. They were the best side and we did not compete.
"Our run of late has been based on hard work, but (against Leicester) we didn't win enough one v one performances. When you have so many players below par, we could have made any number of substitutions.
"It is frustrating, particularly when we have been able to field similar sides over recent games.
"We'll see how the players are in terms of knocks ahead of Portsmouth (today). It's not a time to dwell on a performance like that as there have been more positives than negatives of late.
"But we can't perform like that. It was a million miles away from what we've been producing and it was uncharacteristic of our recent displays."
Eriksson commented: "We deserved to win, we played good football and we haven't won away for a long time. But of course when you have an injury like that it changes the mood.
"What I have learned in this league is that it doesn't really matter who you meet. The difference between the top and bottom teams is nothing, but I would think we could make the play-offs at least if we keep playing like this."
Eriksson said of goalscorer Vassell: "In the first half he played up front on his own and he was brilliant. The pass for the goal was first class and the finish was first class.
"We didn't know if he was going to play because of a back problem. The decision was taken (on the morning of the game), and he was fantastic."
Hull City: Guzan, Rosenior, Zayatte, Gerrard, Dawson, Koren, Ashbee (Bullard 46), Harper, Devitt (Mclean 36), Simpson (McShane 68), Stewart. Unused substitutes: Duke, Barmby, Cullen, Solano.
Leicester City: Weale, Naughton, Morrison, Hobbs, Cunningham (Berner 67), King, Wellens, Abe, Dyer (Oakley 87), Gallagher, Vassell (Waghorn 77). Unused substitutes: Logan, Howard, Moussa, Bednar.
Referee: David Webb (County Durham).