A patchwork Eagles side with 12 players sidelined frustrated Spurs for the vast majority of the game but they allowed Harry Kane to net an 88th minute victor.
But Hodgson said Alli was "no cheat" as he prepared his side to face Spurs at Selhurst Park on Sunday.
A late injury to Tomkins made things even more hard for Palace, with Aurier failing to tuck home into an open goal before Kane shot just wide.
Church of the Holy Sepulcher closes in protest of new policies
Separately, parliament is pursuing a bill that will appropriate lands in Israel sold by churches to anonymous buyers since 2010. She said she does not feel "her mission is accomplished" as she was only visiting for a few days.
Wilfried Zaha is among a number of Eagles' players who will miss the Tottenham game through injuryWhat is the team news?
"So I am happy".
Yet, they will be confident of a win against an Eagles side who have failed to win in four matches and sit just a point above the relegation places.
Tottenham's victory sees them, temporarily at least, move up into the top four, while Palace remain embroiled in a scrap for survival.
Steve Smith will guide Rajasthan Royals in IPL 11
Smith's appointment as captain of the Rajasthan Royals means Ajinkya Rahane missed out on the opportunity. It was a successful season for him as Smith had scored 472 runs in 15 matches in the last IPL season.
The striker had missed two glorious chances as the game looked destined for a goalless draw, but he nodded in Christian Erkisen's last-minute corner for his 24th Premier League goal.
Palace's injury woes were compounded late on when defender James Tomkins went down in innocuous fashion, and his absence was felt when Kane finally headed home the victor with the final whistle fast approaching.
Schlupp had been a key feature of Hodgson's set-up since the former England manager replaced Frank de Boer in September. "If we get the players back that we have unfit at the moment, we know that in our best moments that with our best players we can be quite effective".
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Delpha Capital Management LLC purchased a new position in shares of Royal Bank of Canada in the fourth quarter valued at $151,000. CIBC lowered Royal Bank of Canada from an "outperform" rating to a "neutral" rating in a report on Thursday, February 1st.