Skipper George Boateng insists his Middlesbrough team-mates should take the blame for Saturday's disappointing performance at the Madejski Stadium.
Southgate's name appeared in most of the weekend headlines as his first match as a manager ended in a 3-2 defeat. But Boateng said the onus for team performances should be shifted to the players.
He declared: "I'm tired of all the talk that things are different now that Gareth is in charge. The outside world is making a big issue of it but it's nothing to do with Gareth Southgate. He does what he has to do off the pitch but it is up to the players once the game kicks off. We have to beat the opposition and we didn't do that. We know we have the players and we know we should be winning games like this, especially when we go two goals up, so we are all bitterly disappointed.
"We have a chance to bounce back straight away against Chelsea on Wednesday and we have to take it."
Boateng produced his usual ubiquitous display but Boro were unable to hold on to a two-goal lead and were overwhelmed by Reading's adrenaline-charged fightback. He said: "We made one or two mistakes and we have been punished by a team that was very hungry. We played well in the first 25 minutes and we proved that we have the players who can score goals.
"We might even have got a point in the end. We heard that Mark Viduka's goal wasn't offside. But we are not going to cry over spilt milk. We have to do better."
Boro will definitely be without Julio Arca against Chelsea after the Argentinian took a kick on his foot. The former Sunderland man could be sidelined for two weeks. Southgate can move Austrian international Emanuel Pogatetz out to the flank against the Champions, or bring in teenager Andrew Taylor.
The manager should have centre-back Matthew Bates available again and the teenager is expected to line up alongside Chris Riggott in the heart of the defence - unless Southgate's bid to sign Sylvain Distin is resurrected.
Southgate has refused to pronounce the deal dead, though it could only be revived if Distin was to lower his wage demands.