Everton stole fourth place from Spurs at Goodison Park on Sunday after scoring twice in added time to snatch a dramatic 2-1 victory.
Manchester United and City are on course to once again duel for the title, while Chelsea are favourites to finish third to leave Tottenham battling it out for the final UEFA Champions League place.
"We have to pass one more step to be on the same level as the top three and I don't know when it is going to happen," said Spurs captain Gallas.
"I hope it will be 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.
"For example, Sunday we did almost everything right but they scored that goal which killed us. It is difficult to explain but sometimes you need luck."
Spurs have now conceded 10 goals in the final 15 minutes in league matches this season, and Gallas believes the midweek Europa League win over Panathinaikos took its toll at Everton.
"Was tiredness an issue? Yes," the Frenchman added. "We played on Thursday. Even if we had three days to recover it is not easy, but when you want to win some competitions you have to play every game.
"However, sometimes it is not easy, especially at this time of year because we play so many games but that is not an excuse. What we have to know is that the game is never finished until the referee blows his whistle."
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