The Protectors were held to a 1-1 draw by unfancied Gombak United at the Bishan Stadium on Thursday evening, their second consecutive draw after last week's 0-0 draw against Balestier Khalsa.
And following yet another insipid display, Lim admits Home have plenty of problems he has to address, although he is adamant the blame lies solely with him.
"I take responsibility - we did not play well in these two games, and that is why I'm ashamed of myself," Lee said in his post-match press conference.
"Tonight [Thursday], the players could not handle what I wanted [from them]. We didn't play our game.
"We have problems in defence and attack."
While excuses could have been made for their opening round draw against Balestier, especially with key players Shi Jiayi, John Wilkinson and Qiu Li all missing, the same cannot be said for Thursday's display.
Both Shi and Wilkinson played the full 90 minutes against Gombak, while Qiu was brought on right after halftime.
And Lee believes their most recent performance proved that pre-season talk tipping Home as title challengers was premature.
"We have our key players back," Lee added. "Now that we didn't play well again, I do not know if we need to prepare physically or mentally.
"I need to talk to them [the players]. Maybe if they are physically and mentally stronger, we can play better.
"Now we have shown we are not as strong [as people have made us out to be], having not won our first two games."
And it does not get any easier for Lee as Home's next game is on March 3 at the Choa Chu Kang Stadium against derby rivals SAFFC, who are also hunting for their first win of the season after a draw and a loss against DPMM FC and Balestier respectively.