Those negative results broke a run of improved form which started with a first Premier League win at Everton, holding Chelsea to a goalless draw and then thumping Macclesfield 8-0 in their Carabao Cup tie before beating Manchester United 3-1.
"My first thought at the end is for my player Daniel", he said.
They came very close with an effort from Kelechi Iheanacho, but the goal was disallowed as the young striker was offside.
Leicester laid siege to the West Ham goal thereafter and finally made the breakthrough after 89 minutes with Ndidi's deflected strike making it 1-1. However, Puel would not be drawn on that, saying: "I can't have an opinion".
Saudi Arabia to Prosecute the Killers of Saudi Journalist Khashoggi: Jubeir
Saudi officials have also said he was accidentally killed in a botched security operation to return him to the kingdom. Al-Jubeir said that critics should wait for Saudi Arabia to finish their investigation before blaming anybody.
Nevertheless, Pellegrini thought the progress his side have made was clear to see, adding: "I would answer similar - the same way as I did after the last game which we lost against Tottenham".
Leicester host West Ham in the Premier League on Saturday nine points off the top four.
"Until the final whistle you never know what will be the score". It was really, really hard in the first half although we had more chances.
West Ham manager Manuel Pellegrini said: "I haven't seen the action yet so I can't give my opinion but I will say what I always say when those things happen, it is the decision of the referee. I think that tonight when we are playing eleven against eleven, most part of the game is on their side (half), we dominate actions".
Excluding Vardy from the starting line-up could prove to have disastrous consequences for Puel, and is unlikely to go down well with the club's supporters who have witnessed their club lose four of their last six top-flight games.