Sami Hyypia's men saw their winless run in all competitions extended to six games on Saturday after being held to a 1-1 draw by Hannover in the Bundesliga.
Once title contenders, Leverkusen are 24 points behind league leaders Bayern Munich and the pressure continues to grow on Hyypia.
If not for Leno's fifth-minute penalty save from Szabolcs Huszti, it could have been much worse for Leverkusen.
Gonzalo Castro gave the visitors the lead on 28 minutes but Artjoms Rudnevs equalised for Hannover with a stunning 25-yard effort five minutes later.
Leno said Leverkusen would only start playing their best if they regained much-needed confidence.
"There was a sense of uncertainty on the pitch and you can only get over that by winning games," he said.
"We've got to start doing that straight away."
Leverkusen sporting director Rudi Voller said he felt the nerves in his team after the break.
"We were much too tense in the second half," he said.
Despite their poor run, Leverkusen sit third – five points clear of fifth-placed Wolfsburg in the battle for UEFA Champions League places.
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