The Biancocelesti thought they had secured the three points when Matuzalem broke the deadlock in the 82nd minute, but a stoppage-time Valeri Bojinov strike restored parity.
"We turned in an amazing performance and we did not reap what we sowed because we lacked clarity and maturity in the dying stages, when we could not keep the ball," Reja told Sky Sport Italia.
"The goal came from our distraction and it leaves us bitter because it arrived after we had given more than 100 per cent."
Lazio remain third in the Serie A table, but missed the chance to increase the gap between themselves and Udinese and could see Roma move two points behind them in case of a victory against Juventus.
"This was a decisive match and if we had picked up three points we would have created a good advantage for a Champions League place," the 66-year-old added.
"Udinese, Roma, Napoli and Inter all have a chance to qualify and whoever ends the season in better shape will be able to overcome the others.
"Napoli have the strongest squad and perhaps also the easiest calendar, even though they will face Lecce on Wednesday.
"I still believe Lazio that we can take the third place and I am confident the players from lift themselves up from today's disappointment."