They last tasted victory in front of their own supporters in January but dominated throughout against a stubborn Leicester side.
Simon Church was the chief offender - spurning a number of chances - leaving Waghorn's 45th-minute header as the match winner.
Rodgers said: "I hope I am given time. I've been given a three-year contract but results aren't great, I understand that.
"But that was a good performance.
"I won't feel sorry for myself. I have 100 percent belief in my ability and I remain confident that we can turn it round.
"We played some terrific football but I am very proud of the players.
"There was a lot of pressure on them but they were very good and didn't go missing.
"I try and take the positives from every performance and the public can see that there is lots of great things about our game."
Rodgers saw his side carve open Leicester on numerous occasions but Church and Grzegorz Rasiak were unable to provide a finishing touch.
Rodgers - who started his coaching career with Reading - has hinted at a loan move for a striker but knows that he needs results quickly to save his job.
He said: "You don't need to be a rocket scientist to see that we are lacking something at the top of the pitch.
"We lost a lot of players in the summer and I have given everyone here a chance but we are where we are.
"The only thing missing is the end product.
"Loan signings remain an option and that is something I will have to look at.
"There is criticism and it's not easy. I live in Reading so there is no escape.
"I started badly at Watford but at least I could drive away at the end of each day. I was probably getting the same stick but I couldn't hear it.
"I try not to read the papers and listen to things but when it's your town you can't get away from it.
"It's only a matter of time before we change the atmosphere but we need results."
In contrast, Nigel Pearson saw his side move into the play-off positions with a win which owed much to the performance of goalkeeper Chris Weale as the Foxes kept a fourth clean sheet in five games.
He said: "I'll be the first to admit that our goal at times had a charmed life.
"We were playing a side who were very low in confidence and they were certainly unfortunate.
"Clean sheets are pleasing but we have to play better than that.
"When you don't play well you have to dig in and I thought that even though we weren't at our best we were prepared to stick in there.
"You can't preen your feathers with a win like this but it could prove to be a fantastic result for us."