Last season's champions Chelsea are fifth in the league table with 56 points, five points behind Spurs as both teams bid to qualify for next season's Champions League.
"It's not over until it is mathematically impossible, but it would be very difficult for sure if we lost," Alonso told British media.
"It is definitely a must-win game. Here at Chelsea, we have to fight until the end for every target we can achieve, and next year we have to be in the Champions League. On Sunday, we have to get a win," the Spain international added.
Tottenham have not beaten Chelsea away since 1990, when former England striker Gary Lineker scored the winning goal in a 2-1 league victory.
However, Mauricio Pochettino's Spurs side are unbeaten in the Premier League in 2018, with seven victories and three draws, and come into the mouthwatering clash high on confidence.
"I don't think the past will have an influence. I don't like stats, I think it will be a different game and we will have to give everything and be fully focussed to get the three points," Alonso added.
"It's a massive game. We have a very important target, which is arriving at the end of the season in the top four. Starting on Sunday, it's the first important three points for us."
Tottenham could be without their injured top scorer Harry Kane but Alonso said Chelsea's defenders could still not afford to let their guard down.
"Kane is a very important player for them, that's for sure. But I think they are a very good side physically, with some quality players, and I think it will be a very tough game even without him."
Kane is stepping up his recovery from an ankle injury he picked up in this month's 4-1 win at Bournemouth and will be assessed before the match.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ken Ferris)
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