Ehiogu passed away on Friday after suffering a cardiac arrest at the club's training ground on Thursday afternoon.
The 44-year-old, who coached Spurs' Under-23 side, was honoured with a minute's applause prior to kick-off at Wembley on Saturday while both teams also wore black armbands.
Spurs suffered a 4-2 defeat at the hands of their London rivals, but Pochettino said Ehiogu's death serves as a reminder that sport should pale into insignificance in the aftermath of such tragic news.
"It was Friday and it was a big shock - we were on the training ground," Pochettino said.
"It had a big impact because he was a person who was very close. In that moment you realise real life.
"We are fighting to win games but it's all relative after this situation I want to send my condolences again to friends, family and to all the Tottenham family."
Ehiogu received a flurry of tributes throughout the footballing community while the former defender's wife, Gemma, has set up a fundraising page with the view to starting a charity to help children play football in Ugo's memory.