The 68-year-old said: “I had two top four finishes, we finished fourth twice and should have finished higher in all honesty.
“I thought if we had bought a striker in the last year at Christmas we’d have been very close, I think, to the top. We didn’t invest in a striker at that time. It’s difficult, that top four is difficult.”
Spurs finished fourth in that last season, reaching the FA Cup semi-final and the group stage of the Europa League.
Their Premier League finish would have been good enough to secure Champions League football the following season, except for Chelsea winning the competition, which meant they secured qualification despite a sixth-placed finish.
Spurs impressed that season, but Redknapp has admitted that a new striker was needed to challenge at the top of the league. Jermaine Defoe and Emmanuel Adebayor were the only real consistent goalscorers, although Spurs were aided by the goals of Gareth Bale and Rafael van der Vaart.
If they had signed another striker, it is likely that Spurs would have challenged more competitively, but it is still hard to see them realistically fighting for the title. They ended the campaign on 69 points - which was still 20 behind league winners Manchester City, and second placed United.
Redknapp lost his job at the end of that season, and if a striker was signed he may have secured Champions League football by finishing above Arsenal. However, his claim that he would have challenged at the top seems far off, with the gap in quality evident during the season.