Spurs finished this past campaign in third place and now have Champions League football to look forward to.
The Lilywhites’ task will be to consolidate their position in the top four next term, but Wilkins feels that they could be at a disadvantage from the start.
Tottenham go into next term on the back of a run of four matches without a win, which saw them slip from challenging Leicester City for the title to finishing below their North London rivals, Arsenal.
And Wilkins now has encouraged Tottenham to spend in the summer transfer window, if they are to continue to move forward.
"They had a great season, but the finish was appalling," he said. "To lose 5-1 at Newcastle was an appalling end to the season and it’s always the last game of the season which takes you in to next season.
"You know what the critics are like, and they haven’t won in three games before they start. They have to add to their squad, if they are going to improve."
Tottenham are expected to be active in the summer transfer window, as Daniel Levy is likely to back Mauricio Pochettino with funds.
Pochettino is known to be on the look out for a striker, as he looks to provide competition for Harry Kane.
Spurs are also likely to invest in other areas of their team, as they look to build on the exciting foundations that Pochettino has created at White Hart Lane.