After 12 years at the north London outfit, Walcott struggled to seal a first-team slot under Arsene Wenger and was among Southampton's top targets in the current window but the 28-year-old joined Everton earlier this week.
"I think we did everything to try to bring this possibility here but we have to accept that. It's part of our job," Pellegrino told reporters when asked about Walcott's move.
"When you are in negotiations they are about two parts and we can do nothing.
"Obviously the money is part of the negotiations but I don't know the reason. We have got in our club is the concern to try and bring a couple of targets... We have got another option and we have to continue with our job."
Defender Maya Yoshida missed Southampton's league draw with Watford last weekend due to a hamstring injury and is the only doubt for Pellegrino's side ahead of Saturday's clash with Tottenham Hotspur.
"I think Maya will be a part of Saturday's training session, maybe - but that will be decided tomorrow," Pellegrino added.
Southampton are winless in 10 league games are a point and a place above the relegation zone while Tottenham are fifth.
(Reporting by Aditi Prakash in Bengaluru; Editing by Christian Radnedge)
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