Goals from Rafael van der Vaart, Jermain Defoe and Jake Livermore inside the opening half hour of the play-off first leg were followed up by second-half strikes from Gareth Bale and Aaron Lennon in a comprehensive success.
Redknapp was eager not to openly criticise Scottish football but admitted there was a clear difference between the teams' resources. He said: "I don't want to be disrespectful to Scottish football, but there is obviously a big gulf. It's plain for anybody to see."
He added: "It is a different level now, for sure - it's pretty obvious. Resources are completely different. I've seen some good games, but there's a difference - you look at the money the players earn in the Premier League and the money that's paid in transfers, there's got to be a gulf.
"Listen, we had a good day. We could come here again and it could be different. First half we played ever so well and it was difficult for them."
Spurs were 3-0 up after 28 minutes and Bale and Lennon completed the rout in the second half as time and again the visitors scythed through the Hearts defence. Speaking after the match, Redknapp added: "We started off so well, we moved the ball about fantastic and it was difficult for them to stay with us.
"The movement off the ball, the passing was absolutely top class and that's how I like to see us play. First half it couldn't have gone better."
It was a pleasing display for Redknapp in Spurs' first competitive action of the season and ahead of Monday's Barclays Premier League clash at Manchester United. Redknapp suggested he will have little room to change personnel at Old Trafford and praised the contribution of Niko Kranjcar in central midfield.
The boss added: "He was outstanding."
Redknapp confirmed he could be close to adding to his attacking options, with chairman Daniel Levy in negotiations over a move for Manchester City striker Emmanuel Adebayor. The Spurs boss added: "It seems to have been progressing along and it seems like it probably will happen but I'm not 100% sure."
Source: PA
Source: PA