Both players started the emphatic 5-1 FA Cup semi-final loss to Chelsea on Sunday, and neither could hide their disappointment.
Now the battle for fourth place is set to ensue and neither player seems massively confident about Spurs' chances.
"I think we have to improve a lot," Gallas said. "Even if we have good players and a good squad this result shows we are not ready yet."
Asked if he was worried that the season was falling apart, Gallas added: "Yes, everybody is worried because at the beginning of the season everybody was talking about us, saying we play good football, we can finish third, we are 10 points in front of Arsenal.
"Now we are five points behind them and we have lost the semi-final. It will be difficult because Chelsea and Newcastle are behind us and, after that victory, Chelsea will be very strong. I think they will finish very well so we have to finish well as well."
Gallas confirmed that the managerial issue over whether manager Harry Redknapp would replace Fabio Capello with England has not been a distraction, and the Spurs boss even approached the subject.
"Nobody has been talking about what we will do next season," Gallas said.
"His priority has been to get the team to qualify for the Champions League. So when the people start to speak about him for the national team he came to the dressing room and said: 'Guys, I am very focused on the Champions League and that's it'."
Parker also insisted that the England subject is not a concern for them, saying: "I've not thought about it really.
"It's probably a combination of a few things: a dip in form, a bit of tiredness.
"People are doubting us, whether that be our own fans, even our own manager probably at this moment in time is doubting us a little bit.
"We need to stand up and be counted for, and show the fans, and show him that we're going to try and end up fourth. If we don't end up fourth this year, we will have failed as a squad."