Lampard said it was not "kids football" and there had to be a degree of professionalism in order to get themselves out of their predicament.
Saturday's 2-1 defeat to bottom side Southampton - a 10th defeat in 13 matches in all competitions - saw the club drop to 19th in the table and only staying above Saints on goal difference.
After the game there was a sit-in protest regarding the board's running of the club, while defender Yerry Mina and winger Anthony Gordon were confronted in their cars by angry fans.
But as he prepares for a crucial trip to fellow strugglers West Ham, Lampard urged his squad to focus on what they could do better.
"One of the earliest things I learned in professional football, and maybe my upbringing to be fair, was that the minute you make excuses or try to apportion blame to anything else other than what you can input is the minute you fail," he said.
"The first thing I'd say to the players is not to look anywhere else but themselves.
"And don't get me wrong, I have to manage people not just players. I understand when things are difficult, (there is) a lack of confidence, something is not going right in their game, and I have to mitigate that and try to support and help the players as best I can to get the best performance.
"There is always a balance. You have to tell them when you want them to be better.
"You have to show them, show them what the situation is and what the way out of it is but also try to boost their confidence and that is the job of myself, the staff and the players themselves.
"It is not kids football, there is a lot on, it is a job, it is business, it is professionalism, so you have to find a way out of it.
"It can't all be nice, we have to find things we can improve, but of course we need a confident group to try to get momentum and start getting better results.
"The balance is there for me to try to strike every day I suppose."
Lampard is confident, however, that Mina and Gordon have not been affected after their confrontations last weekend.
Mina got out of his car to speak with some supporters but Gordon remained in his vehicle and attempted to drive through the crowd.
Asked about what impact it had had on those players, Lampard said: "Nothing as far as I know. I've spoken to them both.
"I've been in football a long time, as I keep saying, and I've been at teams where similar things have happened to myself and other players, so let's not make this an Everton conversation.
"When it is a minority of cases of certain incidents now everything gets videoed and becomes viral like it happens every day and that's not necessarily the case.
"I know the majority of Evertonians just want this team to do well and they have a right to voice an opinion but of course we don't want fans going up to the players.
"I think it is a small minority. We don't want that and I'd love to not see that again. But I also understand passionate fans and what they want."