Redmond was left on the bench by Pellegrino at the Vitality Stadium but came on at half-time to set-up Charlie Austin's equaliser in an entertaining 1-1 draw.
Earlier, Ryan Fraser had given Bournemouth the lead just before the interval but Southampton were much-improved after Redmond's introduction.
Pellegrino insisted he had no issue with Pep Guardiola lecturing his player following Wednesday's defeat to Manchester City and he was pleased with Redmond's reaction.
"Am I pleased? Yes, for sure, Nathan is a very important player for us, but after the other day I made six changes because I expected more players to be fresh," Pellegrino said.
"I think he played well and our reaction in the second half was good, especially in the wide areas where we arrived many times making chances."
On whether Redmond felt any extra motivation, Pellegrino added: "I don't think so, it's just a comment, one comment will not change the performance of one player. The most important thing is how we played in the second half."