First-half goals from Sylvan Ebanks-Blake and Richard Stearman - against his former club - put Wolves in control, but Paul Konchesky's 30-yard drive in the 70th minute set up a frantic finale - and only the post prevented Martyn Waghorn rescuing a point for Leicester.
Solbakken said: "You could see that it was a team that is not used to winning. All the good organisation and spells that we had in the first half we lost in the second half. But they fought well, they blocked shots and they were brave in our penalty area and we are relieved that we got three points."
He added: "I think the only way to get confidence is to win games but I think we still need to be braver and to make sure that we are not afraid of playing.
"We have a little way to go with that yet.
"If you are going to be successful you need to have your identity and everyone needs to know what to do when we have and don't have the ball."
Leicester are still without a point away from home this season after three defeats on the road, but manager Nigel Pearson is remaining upbeat - despite being upset by the manner of the goals they let in.
He said: "I am annoyed in the fashion that we conceded goals from two set-plays. It was sloppy and when we had the ball we didn't work hard enough.
"That is not something I have seen from us so far so that was a disappointment. But the players are working hard and I do believe that our fortunes will change.
"There is not an awful lot wrong but we have to start producing winning situations more often and we will do as we have the nucleus of a very good side."
Source: PA
Source: PA