Redknapp tasted FA Cup success with Portsmouth in 2008 and, while admitting it is a "special" competition, insists that a Champions League placing remains his prime objective.
"The cup has always been a special thing and I'd love Tottenham to win it this year, it would be fantastic for us," he said in The Mirror.
"But if we finish in the top four over the season that is probably a great achievement in all honesty, the way it is," he continued.
"It's so tough to do, whereas in the cup you can get the luck of the draws and make it [to the final]. Finishing in the top four over the season is difficult."
Spurs last tasted FA Cup glory almost two decades ago, but the charismatic gaffer insists ousting one of the 'big four' is of greater difficulty given the monopoly the top club's have enjoyed over the years.
He added: "When was the last time Tottenham won? It was 1991. But apart from Everton no-one has been in that top four. No one else has broken in, that's how hard it is and it's going to be just as tough this year because there is real competition.
"Man [Manchester] City are going to be right in there, along with Aston Villa. Our fans would love to see us finish in the top four. The cup winners each year normally come out of that group. Portsmouth broke that mould one year but mostly it's the same teams."
Tottenham face Championship strugglers Peterborough United on Saturday in the world's oldest cup competition.
