The former France international defender won the Premier League with Chelsea twice and refused to blame tiredness or lack of maturity for conceding two late goals in Everton loss.
Manager Andre Villas-Boas had earlier lamented the inability to close out games following the defeat, commenting: "If we count the number of results that have been going for us before the last minutes we would be first."
The north Londoners defeated Panathinaikos in the Europa League on Thursday, but Gallas refused to blame tiredness for the loss, and maintained this was something his team had to overcome in order to progress.
"Was tiredness an issue? Yes," he told The Evening Standard. "But when you want to win some competitions you have to play every game.
"Sometimes it is not easy, especially at this time of year because we play so many games but that is not an excuse. We have to accept the defeat yesterday and we have to carry on."
Gallas won the Premier League twice with Chelsea in 2005 and 2006, but admits he is at a loss to explain why his current side cannot find the same level of consistency.
"I’ve seen the good quality at Tottenham but for some reason, we lose the funny games at home or away and I can’t explain it," he added. "We have to pass one more step to be on the top three and I don’t know when it is going to happen. I hope it will this season but it is a shame because when we get very near, something always happens and we draw or lose.
"In our squad, we have some players that have experience now so I don’t think it is about a lack of maturity. When I was at Chelsea, we had that luck to win some games even if we were not playing good. But Tottenham is different. We gave everything yesterday and had no luck. If you go back, Sigurdsson hit the crossbar and it would then have been 2-0 but it didn’t happen. They scored late and it is very difficult to accept. It is difficult to explain but sometimes you need luck."