The visitors' day was made worse when captain Fabricio Coloccini was sent off for his foul on Suarez.
"We looked comfortable at 1-0 and lacked concentration for their goal," Pardew told Sky Sports News. "It changed proceedings and it has been a bad day for us.
"We looked to keep hitting them on the break, but they are clever and Suarez is a great player. He was causing us problems and if we could have wrapped him up, we would have won the game."
The point means that Newcastle stay in 10th place in the Premier League table.