The Spurs manager insisted that Eriksen, who wants to leave the club, was not starting due to fitness reasons and not to do with his plans to find a new team.
Harry Kane had gone three games without scoring at the Tottenham Hotspur Stadium but he put that right with two goals in four minutes to seal the three points after Tanguy Ndombele cancelled out John McGinn’s early strike.
Pochettino said Eriksen’s 64th minute appearance went a long way to delivering the result.
“Having Christian [Eriksen] fresh with the quality he has helped the team achieve the victory," he said. “In the second half we found different positions and the team started to be more relaxed and be more patient. We were very good. The second half with the same starting 11 in different positions we started to play.”
Lucas Moura should have put Spurs ahead inside the opening five minutes, but he planted a free header at goalkeeper Tom Heaton from Danny Rose's pinpoint cross.
Spurs would have fancied asserting their authority with an early goal, but instead they were picking the ball out of their own net as they were undone by route one in the ninth minute.
Tyrone Mings' long punt caused mayhem and McGinn burst through the acres of space in the Spurs defence and slotted home to give his side the lead.
And Spurs could have found themselves further behind but Trezeguet could not get enough on his shot and Hugo Lloris held with ease.
The start of the second half was much more promising for the hosts as they put Villa under immediate pressure before resorting to bringing Eriksen off the bench and his introduction changed the game.
He began opening Villa up and was involved in Spurs' equaliser as his corner was not cleared properly and Ndombele found the bottom corner from the edge of the area in fine style.
Spurs threw everything at their visitors, who needed Heaton to keep out Eriksen's free-kick, and they eventually got their reward in the 86th minute.
Erik Lamela won the ball back and played in Kane, with the help of a deflection, and the England captain made no mistake from eight yards.
The game was settled in the 90th minute as Kane got his second with a trademark finish from inside the area.
Kane says Tottenham must continue to keep pace with the high standards that Liverpool and Manchester City are setting after both sides scored at will in their opening weekend wins.
"Liverpool set the standard last night, then City this morning so we know it's going to be a tough, long season - we got off to a winning start and there is still lots of things to work on," Kane said.
"The tempo of the game, we came out in the second half with a high tempo, pressed well,” he added. “When Tanguy (Ndombele) got his goal it was full throttle until the end. Thankfully a couple of chances fell to me.
"It's nice to get my first goals here, celebrate in front of the fans. I'm here to work hard for the team and when the chances come put them away.”
Additional reporting by PA
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