England looked good value for victory in normal time at the Spartak Stadium, only for Yerry Mina to pounce in the 93rd minute to prolong the match.
Redknapp has suggested that the introduction of Dier for Tottenham Hotspur teammate Dele Alli almost cost Southgate's men, and he does not want to see the same change made against Sweden if Alli fails to recover from a minor injury.
"Gareth Southgate has been really good in this World Cup, the only backwards step was maybe bringing on Eric Dier," he told Sky Sports News. "Once he came on, I felt we lost the initiative a little bit. We sat back. Jordan Henderson had been looking so good in that defensive midfield role but started to push on.
"We started to make a couple of defensive errors and getting a bit edgy. A substitution like that can say to the players that we're going to hang onto what we've got, and I think that can create a little bit of negativity. In this day and age, it doesn't seem to work that well.
"But I understand why Gareth did it, it's the first thought at the time that you've got to defend and hang onto what you've got, but I thought besides that England were very composed. We are playing against a Sweden side that will sit back, so do you want to bring in an Eric Dier? I think you'd be better off putting an attacking midfield player.
"I thought Ruben Loftus-Cheek caused Tunisia a lot of problems when he came on with his power, and I think he'd give the Swedes a lot of problems. The other ones you look at, if Ashley Young is not fit you've got Fabian Delph or Danny Rose. With [Jamie] Vardy, it's a shame because he's a great impact sub. You'd want him to come off the bench, although you've got [Marcus] Rashford as well."
Vardy is one of a handful of England players carrying a knock from the penalty-shootout win against Colombia.