Lars Bender cancelled out Suleyman Koc's opener before half-time and Leverkusen were expected to go on to win the match after Paderborn's Marvin Bakalorz was sent off with 18 minutes remaining.
Paderborn stunned the BayArena crowd when Moritz Stoppelkamp restored their lead three minutes from time but Leverkusen at least got something from the contest - Karim Bellarabi netting a 90th-minute equaliser.
While Leverkusen lost ground on Bundesliga leaders Bayern Munich, they did enough to remain in the top four.
Schmidt told reporters that Leverkusen struggled to back up from their UEFA Champions League win over Portuguese champions Benfica on Wednesday.
"This was a very difficult game for us," Schmidt said. "The team were a little tired in the legs and tired in the head.
"We were not as consistent as usual at the counter of Paderborn in defence.
"The positive was that the team played better after the substitutions in the second half.
"We were not always smart and intelligent in our play but in the end you have to evaluate the outcome positively."
