Williams admitted his side were 'second best all day long' on a damaging afternoon for the Reds, beaten 3-0 in front of their own supporters and with an injury sustained by Michael Mancienne to add to Eric Lichaj's red card.
It means there is a nine-point gap between Nottingham Forest and MK Dons, currently in the final relegation place, with seven matches remainng in the season.
The first of those is at Reading on Tuesday evening with Williams' demanding a reaction from the players but, if he is not to be in charge next season, the responsiblity for an improved performance lies with those on the field.
Reading moved above the Reds on Saturday with a last-gasp winner at Bolton Wanderers that should secure their safety in the Championship.