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But he was also disappointed in his side's failure to hold onto their lead at 1-0.
After Jack Wilshere put the Gunners ahead, Eden Hazard's spot kick and Marcos Alonso turned the match in the visitor's favour.
But as the enthralling game entered stoppage-time, Bellerin curled home an equaliser to earn his team a point.
The right-back was earlier adjudged to have fouled Chelsea star Hazard by referee Anthony Taylor for Chelsea's penalty.
But Arsenal's 22-year-old wing-back disputed whether his tackle was a foul - as did his manager Arsene Wenger.
"Hazard is very quick in the box and the ball was in the air and I went to challenge for it," Bellerin told the official club website.
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“But we both got there at the same time and the referee thought it was a penalty”
Hector Bellerin
"But we both got there at the same time and the referee thought it was a penalty.
"We will have to see the replay to see what it was like."
Bellerin hadn't found the net for Arsenal since the final day of last season when he opened the scoring against Everton.
And while clearly frustrated to be held to a third draw in four games, he was pleased that the team kept fighting until the very end.
"Well I haven’t scored for a while so it was great to do it in a comeback in a hard-fought game," the Spaniard continued.
Charlie Nicholas' combined Arsenal and Chelsea XI
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"I’m happy with the goal but also happy with the reaction towards the end from the whole team.
"It was non-stop football, running up and down.
"We know when we play them that it is always a hard game, always entertainment.
"We worked hard all week and it is a bit disappointing because we should have held the score [at 1-0 up] but it was a great reaction at the end."
Arsenal face Nottingham Forest in the FA Cup on Sunday (4.00pm).